Monograph records
https://feeds.library.caltech.edu/people/McKelvey-R-D/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 13:58:09 +0000An Experimental Study of the Centipede Game
https://resolver.caltech.edu/CaltechAUTHORS:20160405-154023040
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 1991
We report on a series of experiments in which individuals play a version of the centipede game. In this game, two players alternately get a chance to take the larger portion of a continually escalating pile of money. As soon a.s one person takes, the game ends with that player getting the larger portion of the pile, and the other player getting the smaller portion. If one views the experiment as a complete information game, all standard game theoretic equilibrium concepts predict the first mover should take the large pile on the first round. The experimental results show that this does not occur.
An alternative explanation for the data. can be given if we reconsider the game as a game of incomplete information in which there is some uncertainty over the payoff functions of the players. In particular, if the subjects believe there is some small likelihood that the opponent is an altruist, then in the equilibrium of this incomplete information game, players adopt mixed strategies in the early rounds of the experiment, with the probability of ta.king increasing as the pile gets larger. vVe investigate how well a version of this model explains the data observed in the centipede experiments.https://authors.library.caltech.edu/records/n6131-v8q36Self-correcting Information Cascades
https://resolver.caltech.edu/CaltechAUTHORS:20170731-133225091
Authors: {'items': [{'id': 'Goeree-J-K', 'name': {'family': 'Goeree', 'given': 'Jacob K.'}, 'orcid': '0000-0001-9876-3425'}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}, {'id': 'Rogers-B-W', 'name': {'family': 'Rogers', 'given': 'Brian W.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/3dd4s-jz194
In laboratory experiments, information cascades are ephemeral phenomena, collapsing soon after they form, and then reforming again. These formation/collapse/reformation cycles occur frequently and repeatedly. Cascades may be reversed (collapse followed by a cascade on a different state) and more often than not, such a reversal is self-correcting: the cascade switches from the incorrect to the correct state. Past experimental work focused on relatively short horizons, where these interesting dynamics are rarely observed. We present experiments with a longer horizon, and also investigate the effect of signal informativeness. We propose a theoretical model, based on quantal response equilibrium, where temporary and self-correcting cascades arise as equilibrium phenomena. The model also predicts the systematic differences we observe experimentally in the dynamics, as a function of signal informativeness. We extend the basic model to include a parameter measuring base rate neglect and find it to be a statistically significant factor in the dynamics, resulting in somewhat faster rates of social learning.https://authors.library.caltech.edu/records/3dd4s-jz194A Theory of Voting in Large Elections
https://resolver.caltech.edu/CaltechAUTHORS:20170810-163456027
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Patty-J-W', 'name': {'family': 'Patty', 'given': 'John W.'}}]}
Year: 2017
DOI: 10.7907/5pq1n-gsc34
This paper provides a game-theoretic model of probabilistic voting and then examines the incentives faced by candidates in a spatial model of elections. In our model, voters' strategies form a Quantal Response Equilibrium (QRE), which merges strategic voting and probabilistic behavior. We first show that a QRE in the voting game exists for all elections with a finite number of candidates, and then proceed to show that, with enough voters and the addition of a regularity condition on voters' utilities, a Nash equilibrium profile of platforms exists when candidates seek to maximize their expected margin of victory. This equilibrium (1) consists of all candidates converging to the policy that maximizes the expected sum of voters' utilities, (2) exists even when voters can abstain, and (3) is unique when there are only 2 candidates.https://authors.library.caltech.edu/records/5pq1n-gsc34Status Quo Bias in Bargaining: An extension of the Myerson Satterthwaite Theorem with an application to the Coase Theorem
https://resolver.caltech.edu/CaltechAUTHORS:20170811-153048325
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Page-T', 'name': {'family': 'Page', 'given': 'Talbot'}}]}
Year: 2017
DOI: 10.7907/fykjr-x5418
We use a generalized version of the Myerson-Satterthwaite theorem to study inefficiencies in bilateral bargaining over trade of an indivisible good, where there is two sided private information on the valuations. We show that when preferences are convex and quasi linear, and when the private information represents the magnitude of the utility gain or loss and follows a uniform distribution, that the most efficient mechanism always exhibits a bias towards the status quo. In the case that utility functions are quadratic in the amount traded, we prove that for any incentive compatible direct mechanism, there is an expected bias towards the disagreement point. In other words, for the class of preferences we study, there is a strategic advantage to property rights in the Coase bargaining setup in the presence of incomplete information.https://authors.library.caltech.edu/records/fykjr-x5418An Experimental Study of Jury Decision Rules
https://resolver.caltech.edu/CaltechAUTHORS:20170811-153843207
Authors: {'items': [{'id': 'Guarnaschelli-S', 'name': {'family': 'Guarnaschelli', 'given': 'Serena'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/49qpb-78b68
We present experimental results on individual decisions in juries. We consider the effect of three treatment variables: the size of the jury (three or six), the number of votes needed for conviction (majority or unanimity), and jury deliberation. We find evidence of strategic voting under the unanimity rule, where the form of strategic behavior involves a bias to vote guilty to compensate for the unanimity requirement. A large fraction of jurors vote to convict even when their private information indicates the defendant is more likely to be innocent than guilty. This is roughly consistent with the game theoretic predictions of Feddersen and Pesendorfer (FP) [1998]. While individual behavior is explained well by the game theoretic model, at the level of the jury decision, there are numerous discrepancies. In particular, contrary to the FP prediction, we find that in our experiments juries convict fewer innocent defendants under unanimity rule than under majority rule. We are able to simultaneously account for the individual and group data by using Quantal Response Equilibrium to model the error.https://authors.library.caltech.edu/records/49qpb-78b68An Experimental Study of the Effect of Private Information in the Coase Theorem
https://resolver.caltech.edu/CaltechAUTHORS:20170814-133129502
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Page-T', 'name': {'family': 'Page', 'given': 'Talbot'}}]}
Year: 2017
DOI: 10.7907/h25ge-vez95
This paper investigates, in an experimental setting, the effect of private information on the Coase theorem's predictions of efficiency and allocative neutrality. For a two-person bargaining game, we find significantly more inefficiency and allocative asymmetry in the case of private information compared with the case of complete information. We also find substantial bargaining breakdown, which is not predicted by the Coase theorem. For the case of private information, the Coase theorem does not predict as well as a generalized version of the Myerson-Satterthwaite theorem, which predicts inefficiency, allocative non-neutrality in the direction of the disagreement point, and some bargaining breakdown.https://authors.library.caltech.edu/records/h25ge-vez95The Effects of Payoff Magnitude and Heterogeneity on Behavior in 2 x 2 Games with Unique Mixed Strategy Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20170815-143845609
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}, {'id': 'Weber-R-A', 'name': {'family': 'Weber', 'given': 'Roberto A.'}}]}
Year: 2017
DOI: 10.7907/95xv9-jkv06
The Logit version of Quantal Response Equilibrium predicts that equilibrium behavior in games will vary systematically with payoff magnitudes, if all other factors are held constant (including the Nash equilibria of the game). We explore this in the context of a set of asymmetric 2x2 games with unique totally mixed strategy equilibria. The data provide little support for the payoff magnitude predictions of the Logit Equilibrium model. We extend the theoretical Quantal Response Equilibrium model to allow for heterogeneity, and find that the data fit the heterogeneous version of the theory significantly better.https://authors.library.caltech.edu/records/95xv9-jkv06A Statistical Theory of Equilibrium in Games
https://resolver.caltech.edu/CaltechAUTHORS:20170816-165243053
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/m8276-pad75
This paper describes a statistical model of equilibrium behavior in games, which we call Quanta! Response Equilibrium (QRE). The key feature of the equilibrium is that individuals do not always play best responses to the strategies of their opponents, but play better strategies with higher probability than worse strategies. We illustrate several different applications of this approach, and establish a number of theoretical properties of this equilibrium concept. We also demonstrate an equivalence between this equilibrium notion and Bayesian games derived from games of complete information with perturbed payoffs.https://authors.library.caltech.edu/records/m8276-pad75Quantal Response Equilibria for Extensive Form Games
https://resolver.caltech.edu/CaltechAUTHORS:20170817-143555993
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/prxgj-mg253
This paper investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal choice model, and assume other players do so as well. We define an Agent Quantal Response Equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal choice probabilities are given by logit response functions.
AQRE makes predictions that contradict the invariance principle in systematic ways. We show that these predictions match up with some experimental findings by Schotter, Weigelt and Wilson (1993) about the play of games that differ only with respect to inessential transformations of the extensive form. The logit-AQRE also implies a unique selection from the set of subgame perfect equilibria in generic extensive form games. We examine data from signalling game experiments by Banks, Camerer, and Porter (1994) and Brandts and Holt (1993). We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these experiments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment.https://authors.library.caltech.edu/records/prxgj-mg253A Liapunov Function for Nash Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20170817-134102962
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/f61vr-arf47
In this paper, I construct a Liapunov function for Nash equilibria for finite n–person games in normal form. This function is useful for computation of Nash equilibria, since it converts the problem into a standard minimization problem. It provides an alternative to existing computational methods, which are based either on n - person extensions of the algorithm of Lemke and Howson [1961] (eg., Wilson [1971] and Rosenmiiller [1971]), or on methods for finding the fixed point of the best response correspondence, such as simplicial division algorithms (eg., Todd [1976], and Van der Laan et al. [1987]). This work is also related to that of Brown and von Neumann [1950], and Rosen [1964], who construct differential equation systems for solving certain classes of games.https://authors.library.caltech.edu/records/f61vr-arf47An Experimental Study of Constant-sum Centipede Games
https://resolver.caltech.edu/CaltechAUTHORS:20170823-133811016
Authors: {'items': [{'id': 'Fey-M', 'name': {'family': 'Fey', 'given': 'Mark'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/g1kfx-nex14
In this paper, we report the results of a series of experiments on a version of the centipede game in which the total payoff to the two players is constant. Standard backward-induction arguments lead to a unique Nash equilibrium outcome prediction, which is the same as the prediction made by theories of "fair" or "focal" outcomes.
We find that subjects frequently fail to select the unique Nash outcome prediction. While this behavior was also observed in McKelvey and Palfrey (1992) in the "growing pie" version of the game they studied, the Nash outcome was not "fair", and there was the possibility of Pareto improvement by deviating from Nash play. Their findings could therefore be explained by small amounts of altruistic behavior. There are no Pareto improvements available in the constant-sum games we examine, hence explanations based on altruism cannot account for these new data.
We examine and compare two classes of models to explain this data. The first class consists of non-equilibrium modifications of the standard "Always Take" model. The other class we investigate, the Quanta! Response Equilibrium model, describes an equilibrium in which subjects make mistakes in implementing their best replies and assume other players do so as well. One specification of this model fits the experimental data best, among the models we test, and is able to account for all the main features we observe in the data.https://authors.library.caltech.edu/records/g1kfx-nex14The Maximal Number of Regular Totally Mixed Nash Equilibria
https://resolver.caltech.edu/CaltechAUTHORS:20170823-152433647
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'McLennan-A', 'name': {'family': 'McLennan', 'given': 'Andrew'}}]}
Year: 2017
DOI: 10.7907/w4xpy-8z371
Let S=∏^n_(i=1) Si be the strategy space for a finite n-person game. Let (S10,…, Sn0) ϵ S be any strategy n-tuple, and let Ti = Si - {si0}, i = 1, ..., n. We show that the maximum number of regular totally mixed Nash equilibria to a game with strategy sets Si is the number of partitions P = {P1,…, Pn} of UiTi such that, for each i, #Pi = #Ti and Pi ∩ Ti = ∅. The bound is tight, as we give a method for constructing a game with the maximum number of equilibria.https://authors.library.caltech.edu/records/w4xpy-8z371The Holdout Game: An Experimental Study of an Infinitely Repeated Game with Two-Sided Incomplete Information
https://resolver.caltech.edu/CaltechAUTHORS:20170829-134803360
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/h5sgq-1q935
We investigate experimentally a two-person infinitely repeated game of incomplete information. In the stage game, each player chooses to give in or hold out. Players have privately known costs of giving in and each player receives a fixed benefit whenever at least one player gives in. High cost players have a dominant strategy in the stage game to hold out, and the low cost players ' best response depends on what the opponent does. Equilibrium play to the infinitely repeated game conveys information about the players' type.
We investigate two questions: whether there is any evidence that subject behavior approximates belief stationary equilibria, and whether there is evidence that subjects will converge to an equilibrium of the correct state. We conclude that subjects do not adopt symmetric belief stationary strategies for the holdout game. However, we cannot reject the hypotheses that subjects converge towards eventually playing an equilibrium of the correct state (even though they do not always learn the correct state). Behavior of experienced subjects is closer to the predictions of symmetric belief-stationary equilibrium.https://authors.library.caltech.edu/records/h5sgq-1q935Stationarity and Chaos in Infinitely Repeated Games of Incomplete Information
https://resolver.caltech.edu/CaltechAUTHORS:20170829-135834135
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/kz8hk-4de75
Consider an incomplete information game in which the players first learn their own types, and then infinitely often play the same normal form game with the same opponents. After each play, the players observe their own payoff and the action of their opponents. The payoff for a strategy n-tuple in the infinitely repeated game is the discounted present value of the infinite stream of payoffs generated by the strategy. This paper studies Bayesian learning in such a setting. Kalai and Lehrer [1991] and Jordan [1991] have shown that Bayesian equilibria to such games exist and eventually look like Nash equilibria to the infinitely repeated full information game with the correct types. However, due to folk theorems for complete information games, this still leaves the class of equilibria for such games to be quite large.
In order to refine the set of equilibria, we impose a restriction on the equilibrium strategies of the players which requires stationarity with respect to the profile of current beliefs: if the same profile of beliefs is reached at two different points in time, the players must choose the same behavioral strategy at both points in time. This set, called the belief stationary equilibria, is a subset of the Bayesian Nash equilibria. We compute a belief stationary equilibrium in an example. The equilibria that result can have elements of chaotic behavior. The equilibrium path of beliefs when types are not revealed can be chaotic, and small changes in initial beliefs can result in large changes in equilibrium actions.https://authors.library.caltech.edu/records/kz8hk-4de75Political Competition in a Model of Economic Growth; Some Theoretical Results
https://resolver.caltech.edu/CaltechAUTHORS:20170830-135904085
Authors: {'items': [{'id': 'Boylan-R-T', 'name': {'family': 'Boylan', 'given': 'Richard T.'}}, {'id': 'Ledyard-J-O', 'name': {'family': 'Ledyard', 'given': 'John O.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/dja9h-egh71
We study a one-sector model of economic growth in which decisions about capital accumulation and consumption are made through a political process of two candidate competition. Each voter's utility for a consumption stream is the discounted value of that voter's utility of consumption in each period. We consider the case when voters' one period utility functions for consumption are identical but discount factors are different. We are particularly interested in the conditions under which neoclassical optimal growth paths occur, and conditions in which political business cycles occur.
The answer depends on the ability or inability of the candidates to commit to multi-period investment strategies. If candidates can commit indefinitely into the future, then a political (majority rule) equilibrium path will not exist if all discount factors are different. For any feasible consumption path, there is a perturbation which is majority preferred to it. For any neoclassical optimal path there exists a perturbated path that is preferred to it either unanimously or by all but one voter. These results are true even if the perturbations can differ at no more than three consecutive periods from the original path.
If candidates are unable to commit to multi-period plans, we show there is a unique subgame perfect, stationary, symmetric equilibrium to the infinite horizon two candidate competition game; namely the optimal consumption path for the median voter. The equilibrium is unique in the following sense: It is the unique limit of subgame perfect equilibria to the finite horizon electoral game.
In the case when candidates can commit for a finite time into the future, we show that a stationary minmax path (a path which minimizes the maximum vote that can be obtained against it) yields a political business cycle.https://authors.library.caltech.edu/records/dja9h-egh71Initial Versus Continuing Proposal Power in Legislative Seniority
https://resolver.caltech.edu/CaltechAUTHORS:20170830-153142114
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Reizman-R-G', 'name': {'family': 'Reizman', 'given': 'Raymond G.'}}]}
Year: 2017
DOI: 10.7907/w9sq4-wzr65
We compare two different seniority systems in a legislature whose sole task is to decide on distributive issues, and which operates under a Baron-Ferejohn recognition rule, where recognition probability is based on seniority. In the first system, called "initial proposal power", recognition probability for the initial proposal is based on seniority, but once the proposal is voted on by the legislature, all members have equal recognition probabilities for any reconsideration. Under the second system, called "continuing proposal power,'' seniority is used to determine proposal power both in the initial consideration and in any reconsideration. We find that in the case of seniority systems embodying continuing proposal power, there does not exist an equilibrium in which incumbents are reelected, and in which legislators would endogenously choose to impose such a seniority system on themselves. This contrasts with previous results in which we have shown that there does exist such an equilibrium for the case of initial proposal power. The reason for this result is that continuing proposal power lowers the value of senior members, since it makes them less desirable as coalition partners.https://authors.library.caltech.edu/records/w9sq4-wzr65Engodeneity of Alternating Offers in a Bargaining Game
https://resolver.caltech.edu/CaltechAUTHORS:20170823-134601561
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/46qat-kfm09
We investigate an infinite horizon two-person simultaneous offer bargaining game of incomplete information with discounted playoffs. In each period, each player chooses to give in or hold out. The game continues until at least one of the players chooses to give in, at which point agreement has been reached and the game terminates, with an agreement benefit accruing to each player, and a cost to the player (or players) that give in. Players have privately known agreement benefits. 'Low benefit players have a weakly dominant strategy to hold out forever; high benefit players would be better off giving in if they knew their opponent was planning to hold out forever.
For any discount factor there is a unique Nash equilibrium in which the two players alternate in their willingness to give in, if the players' priors about each others type are sufficiently asymmetric. Second, for almost all priors, this is the unique equilibrium if the discount factor is close enough to one.https://authors.library.caltech.edu/records/46qat-kfm09A Bayesian Sequential Experimental Study of Learning in Games
https://resolver.caltech.edu/CaltechAUTHORS:20170831-141309234
Authors: {'items': [{'id': 'El-Gamal-M', 'name': {'family': 'El-Gamal', 'given': 'Mahmoud'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Palfrey-T-R', 'name': {'family': 'Palfrey', 'given': 'Thomas R.'}, 'orcid': '0000-0003-0769-8109'}]}
Year: 2017
DOI: 10.7907/hgs8z-hwd27
We apply a sequential Bayesian sampling procedure to study two models of learning in repeated games. The first model is that individuals learn only about an opponent when they play her/him repeatedly, but do not update from their experience with that opponent when they move on to play the same game with other opponents. We label this the non-sequential model. The second model is that individuals use Bayesian updating to learn about population parameters from each of their opponents, as well as learning about the idiosyncrasies of that particular opponent. We call that the sequential model.
We sequentially sample observations on the behavior of experimental subjects in the so called 'centipede game'. This game has the property of allowing for a trade-off between competition and cooperation, which is of interest in many economic situations. At each point in time, the 'state' of our dynamic problem consists of our beliefs about the two models, and beliefs about the nuisance parameters of the two models. Our 'choice' set is to sample or not to sample one more data point, and if we should not sample, which of the models to select. After 19 matches (4 subjects per match), we stop and reject the non-sequential model in favor of the sequential model.https://authors.library.caltech.edu/records/hgs8z-hwd27Seniority in Legislatures
https://resolver.caltech.edu/CaltechAUTHORS:20170901-140827674
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Reizman-R-G', 'name': {'family': 'Reizman', 'given': 'Raymond G.'}}]}
Year: 2017
DOI: 10.7907/af878-br061
We construct a stochastic game model of a legislature with an endogenously determined seniority system. We model the behavior of the legislators as well as their constituents in an infinitely repeated divide the dollar game. Each legislative session must make a decision on redistributional issues, modeled as a divide the dollar game. However, each session begins with a vote in which the legislators decide, by majority rule, whether or not to impose on themselves a seniority system. Legislative decisions on the redistributional issues are made by the Baron-Ferejohn rule: an agenda setter is selected by a random recognition rule (which in our model is a function of the seniority system selected), the agenda setter makes a proposal on redistributional issues, and the legislature then votes whether to accept or reject the agenda setters proposal. If the legislature rejects the proposal, another agenda setter is randomly selected, and the process is repeated. If the legislature accepts the proposal, the legislative session ends, and the voters in each legislative district vote whether to retain their legislator or throw it out of office. The voters' verdict determines the seniority structure of the next period legislature. We find a stationary equilibrium to the game having the property that the legislature imposes on itself a non trivial seniority system, and that legislators are always reelected.https://authors.library.caltech.edu/records/af878-br061Public and Private Information: An Experimental Study of Information Pooling
https://resolver.caltech.edu/CaltechAUTHORS:20170905-141058732
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Page-T', 'name': {'family': 'Page', 'given': 'Talbot'}}]}
Year: 2017
DOI: 10.7907/t4jca-fps61
This paper reports on an experimental study of-the way in which individuals make inferences from publicly available information. We compare the predictions of a theoretical model of a common knowledge inference process with actual behavior. In the theoretical model, "perfect Bayesians," starting with private information, take actions; an aggregate statistic is made publicly available; the individuals do optimal Bayesian updating and take new actions; and the process continues until there is a common knowledge equilibrium with complete information pooling. We find that the theoretical model roughly predicts the observed behavior, but the actual inference process is clearly less efficient than the standard of the theoretical model, and while there is some pooling, it is incomplete.https://authors.library.caltech.edu/records/t4jca-fps61A Decade of Experimental Research on Spatial Models of Elections and Committees
https://resolver.caltech.edu/CaltechAUTHORS:20170907-153928970
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Ordeshook-P-C', 'name': {'family': 'Ordeshook', 'given': 'Peter C.'}}]}
Year: 2017
DOI: 10.7907/bc0gn-qhp30
The Euclidean representation of political issues and alternative outcomes, and
the associated representation of preferences as quasi-concave utility functions is by
now a staple of formal models of committees and elections. This theoretical
development, moreover, is accompanied by a considerable body of experimental research.
We can view that research in two ways: as a test of the basic propositions about
equilibria in specific institutional settings, and as an attempt to gain insights into
those aspects of political processes that are poorly understood or imperfectly
modeled, such as the robustness of theoretical results with respect to procedural
details and bargaining environments. This essay reviews that research so that we can
gain some sense of its overall import.https://authors.library.caltech.edu/records/bc0gn-qhp30Game Forms for Nash Implementation of General Social Choice Correspondences
https://resolver.caltech.edu/CaltechAUTHORS:20170915-133024179
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/a7ntz-bnj28
Several game forms are given for implementing general social choice correspondences (SCC's) which satisfy Haskin's conditions of monotonicity and No Veto Power. The game forms have smaller strategy spaces than those used in previously discovered mechanisms: the strategy for an individual consists of an alternative, two subsets (of alternatives), and a player number. For certain types of economic and political SCC's, including a-majority rule, the Walrasian, and Lindahl correspondence, the strategy space reduces to an alternative and a vector, where the number of components of the vector is at most twice the dimension of the alternative space.https://authors.library.caltech.edu/records/a7ntz-bnj28Structural Instability of the Core
https://resolver.caltech.edu/CaltechAUTHORS:20170908-145130668
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Schofield-N', 'name': {'family': 'Schofield', 'given': 'Norman'}}]}
Year: 2017
DOI: 10.7907/e2cny-p7059
Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)=2q-n+1 and let W be a smooth 'policy space' of dimension w. Let U〖(W)〗^N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an 'instability dimension' w*(σ) with 2≦w*(σ)≦w(n,q) such that:
1. (i) if w≧w*(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)N (i.e., almost always),
2. (ii) if w≧w*(σ)+1, and W has a boundary, then the core of σ is empty, almost always,
3. (iii) if w≧w*(σ)+1, then the cycle set is dense in W, almost always,
4. (iv) if w≧w*(σ)+2 then the cycle set is also path connected, almost always.
The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of 'pivotal' coalitions of size 2q-n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1.https://authors.library.caltech.edu/records/e2cny-p7059Sequential Elections with Limited Information
https://resolver.caltech.edu/CaltechAUTHORS:20170919-152059788
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Ordeshook-P-C', 'name': {'family': 'Ordeshook', 'given': 'Peter C.'}}]}
Year: 2017
DOI: 10.7907/v23kd-qbn10
We develop theoretically and test experimentally a one dimensional model of two candidate competition with incomplete information. We consider a sequence of elections in which the same general issue predominates from election to election, but where the voters have no contemoporaneous information about the policy positions adopted by the candidates, and where the candidates have no contemporaneous information about the preferences of the voters. Instead, participants have access only to contemporaneous endorsement data of an interest group, and to historical policy positions of the previous winning candidates. We define a stationary rational expectations equilibrium to the resulting (repeated) game of incomplete information, and show that in equilibrium, all participants, voters and candidates alike, end up acting as if they had complete information: Voters end up voting for the correct candidate, and candidates end up converging to the median voter.https://authors.library.caltech.edu/records/v23kd-qbn10Optimal Research for Cournot Oligopolists
https://resolver.caltech.edu/CaltechAUTHORS:20170915-164128100
Authors: {'items': [{'id': 'Li-Lode', 'name': {'family': 'Li', 'given': 'Lode'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Page-T', 'name': {'family': 'Page', 'given': 'Talbot'}}]}
Year: 2017
DOI: 10.7907/jdn82-4bs44
We extend the classical Cournot model to take account of uncertainty in either the cost function or the demand function. By undertaking research, firms can acquire private (asymmetric) information to help resolve their uncertainty and make a more informed production decision. The model is a two stage game: in the first stage research levels are chosen, and in the second stage, conditional on private research outcomes, production decisions are made.
We find that for a linear, continuous information structure there is a unique Nash equilibrium to the game. In the equilibrium there may be an inefficient amount of aggregate research and there may be incomplete pooling as well.
The model specializes to the classical case when the cost of research is zero (and each firm gains essentially the same information by doing an infinite amount of research) or when the cost of research is so high no firm undertakes research.https://authors.library.caltech.edu/records/jdn82-4bs44Generalized Symmetry Conditions at a Core Point
https://resolver.caltech.edu/CaltechAUTHORS:20170918-145109056
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Schofield-N', 'name': {'family': 'Schofield', 'given': 'Norman'}}]}
Year: 2017
DOI: 10.7907/scsnd-3xh89
Previous analyses have shown that if a point x is to be a core of a majority rule voting game in Euclidean space, when preferences are smooth, then the utility gradients must satisfy certain restrictive symmetry conditions. In this paper these results are generalized to the case of an arbitrary voting rule, and necessary and sufficient conditions, expressed in terms of "pivotal" coalitions, are obtained.https://authors.library.caltech.edu/records/scsnd-3xh89Elections with Limited Information: A Multidimensional Model
https://resolver.caltech.edu/CaltechAUTHORS:20170919-154054641
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Ordeshook-P-C', 'name': {'family': 'Ordeshook', 'given': 'Peter C.'}}]}
Year: 2017
DOI: 10.7907/ebpx6-ssr61
We develop a game theoretic model of 2 candidate competition over a multidimensional policy space, where the participants have incomplete information about the preferences and strategy choices of other participants. The players consist of the voters and the candidates. Voters are partitioned into two classes, depending on the information they observe. Informed voters observe candidate strategy choices while uninformed voters do not. All players (voters and candidates alike) observe contemporaneous poll data broken down by various subgroups of the population.
The main results of the paper give conditions on the number and distribution of the informed and uninformed voters which are sufficient to guarantee that any equilibrium (or voter equilibrium) extracts all information.https://authors.library.caltech.edu/records/ebpx6-ssr61Covering, Dominance, and Institution Free Properties of Social Change
https://resolver.caltech.edu/CaltechAUTHORS:20170921-143236008
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/ktzhs-d3673
This paper shows that different institutional structures for aggregation of preferences under majority rule may generate social choices that are quite similar, so that the actual social choice may be rather insensitive to the choice of institutional rules. Specifically, in a multidimensional setting, where all voters have strictly quasi concave preferences, it is shown that the "uncovered set" contains the outcomes that would arise from equilibrium behavior under three different institutional settings. The three institutional settings are two candidate competition in a large electorate, cooperative behavior in small committees, and sophisticated voting behavior in a legislative environment where the agenda is determined endogenously. Because of its apparent institution free properties, the uncovered set may provide a useful generalization of the core when a core does not exist. A general existence theorem for the uncovered set is proven, and for the Downsian case, bounds for the uncovered set are computed. These bounds show that the uncovered set is centered around a generalized median set whose size is a measure of the degree of symmetry of the voter ideal points.https://authors.library.caltech.edu/records/ktzhs-d3673Common Knowledge and Consensus with Aggregate Statistics
https://resolver.caltech.edu/CaltechAUTHORS:20170921-144910869
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Page-T', 'name': {'family': 'Page', 'given': 'Talbot'}}]}
Year: 2017
DOI: 10.7907/z43xd-96j96
We prove that if n individuals start with the same prior over a probability space, and then each observe private information that for a class of admissible statistics, if a statistic of their posterior probabilities of an event becomes common knowledge, then everyone's posterior probabilities must be the same. The class of admissible statistics includes any statistic which is an invertible function of a stochastically monotone function. We also prove that if information partitions are finite, an iterative procedure of public announcement of the statistic—where the statistic is publicly announced and then individuals recompute posterior probabilities based on their previous information plus the announced value of the statistic—converges in a finite number of steps to the common knowledge situation described above. The result has applications to Delphi type processes for probability assessment, and to economic models in which private information becomes incorporated into an aggregate, publicly observed statistic such as a price or quantity in a market.https://authors.library.caltech.edu/records/z43xd-96j96Elections with Limited Information: A Fulfilled Expectations Model Using Contemporaneous Poll and Endorsement Data as Information Sources
https://resolver.caltech.edu/CaltechAUTHORS:20171002-152708822
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Ordeshook-P-C', 'name': {'family': 'Ordeshook', 'given': 'Peter C.'}}]}
Year: 2017
DOI: 10.7907/a7hd5-zy507
This paper is one of several papers in which we develop and test models of 2 candidate elections under extremely decentralized and incomplete information conditions. We assume candidates do not know voter utility functions, and that most voters do not observe the policy positions adopted by the candidates, We assume that uninformed actors (voters and candidates alike) have "beliefs" about parameters of which they are uninformed, and that they attempt to inform these beliefs on the basis of readily observable variables endogenous to the system. Specifically, in this paper, we assume that uninformed actors inform their beliefs, and hence condition their behavior, on the basis of contemporaneous poll and (binary) endorsement data. An equilibrium is defined to be a set of strategies, together with a set of beliefs, such that all actors are maximizing expected utility subject to their beliefs, and such that no actor wants to revise his beliefs conditional on the information he does observe. This paper develops the above model only for the case of a one dimensional policy space with symmetric single peaked preferences.
When the electorate is modeled as being infinite, with the cumulative density of ideal points for both informed and uninformed voters being invertible, we show that regardless of the number of informed voters, in an equilibrium, the candidates behave exactly as if all voters have complete information. They respond to the preferences of the uninformed as well as the informed voters, ending up at the median ideal point of the entire electorate. Further, we show that regardless of candidate behavior, if voters are in equilibrium, their votes will extract all available information, in the sense that all voters, informed and uninformed alike, will vote as if they had perfect information about candidate positions. Finally, we give a dynamic for convergence of voting behavior, which shows that the model implies a "bandwagon" effect, with the speed of convergence depending on the ratio of the density of informed to uninformed voters at the true candidate midpoint.
In addition to the theoretical results, we run some experiments to test the implications of the model. The experiments show a moderate degree of support for the model.https://authors.library.caltech.edu/records/a7hd5-zy507Methods for Comparison of Markov Processes by Stochastic Dominance
https://resolver.caltech.edu/CaltechAUTHORS:20171004-164948358
Authors: {'items': [{'id': 'Green-E-J', 'name': {'family': 'Green', 'given': 'Edward J.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Packel-E-W', 'name': {'family': 'Packel', 'given': 'Edward W.'}}]}
Year: 2017
DOI: 10.7907/em073-25e98
A technique is developed for proving existence and obtaining bounds for the concentration of a stationary distribution for a given Markov process on the basis of comparisons, via stochastic dominance, with a different Markov process, having a known stationary distribution.https://authors.library.caltech.edu/records/em073-25e98Limiting Distributions for Continuous State Markov Voting Models
https://resolver.caltech.edu/CaltechAUTHORS:20171004-165602546
Authors: {'items': [{'id': 'Ferejohn-J-A', 'name': {'family': 'Ferejohn', 'given': 'John A.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Packel-E-W', 'name': {'family': 'Packel', 'given': 'Edward W.'}}]}
Year: 2017
DOI: 10.7907/p4th4-s2326
This paper proves the existence of a stationary distribution for a class of Markov voting models. We assume that alternatives to replace the current status quo arise probabilistically, with the probability distribution at time t+1 having support set equal to the set of alternatives that defeat, according to some voting rule, the current status quo at time t. When preferences are based on Euclidean distance, it is shown that for a wide class of voting rules, a limiting distribution exists. For the special case of majority rule, not only does a limiting distribution always exist, but we obtain bounds for the concentration of the limiting distribution around a centrally located set. The implications are that under Markov voting models, small deviations from the conditions for a core point will still leave the limiting distribution quite concentrated around a generalized median point. Even though the majority relation is totally cyclic in such situations, our results show that such chaos is not probabilistically significant.https://authors.library.caltech.edu/records/p4th4-s2326A Ham Sandwich Theorem for General Measures
https://resolver.caltech.edu/CaltechAUTHORS:20171009-163353049
Authors: {'items': [{'id': 'Cox-G-W', 'name': {'family': 'Cox', 'given': 'Gary W.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/c09md-7bk98
The "ham sandwich" theorem has been proven only for measures that are absolutely continuous with respect to Lesbeque measure. We prove a generalized version of the ham sandwich theorem which is applicable to arbitrary finite measures, and we give some sufficient conditions for uniqueness of the hyperplane identified by the theorem.https://authors.library.caltech.edu/records/c09md-7bk98Implementation of Democratic Social Choice Functions
https://resolver.caltech.edu/CaltechAUTHORS:20171013-145311553
Authors: {'items': [{'id': 'Ferejohn-J-A', 'name': {'family': 'Ferejohn', 'given': 'John A.'}}, {'id': 'Grether-D-M', 'name': {'family': 'Grether', 'given': 'David M.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.2307/2297367
A social choice function is said to be implementable if and only if there exists a game form such that for all preference profiles an equilibrium strategy n-tuple exists and any equilibrium strategy n-tuples of the game yield outcomes in the social choice set. A social choice function is defined to be minimally democratic if and only if whenever there exists an alternative which is ranked first by n-1 voters and is no lower than second for the last voter, then the social choice must be uniquely that alternative. No constraints are placed on the social choice function for other preference profiles.
Using the usual definitions of equilibria for n-person games—namely Nash and strong equilibria—it is shown here that over unrestricted preference domains, no minimally democratic social choice function is implementable. The same result holds in certain restricted domains of the type assumed by economists over public goods spaces. We then show that a different notion of equilibrium—namely that of sophisticated equilibrium—allows for implementation of democratic social choice functions also having further appealing properties. The implication is that models of democratic political processes cannot be based on the standard equilibrium notions of Nash or strong equilibria.https://authors.library.caltech.edu/records/jpr5r-tm813A Theory of Optimal Agenda Design
https://resolver.caltech.edu/CaltechAUTHORS:20171017-142454970
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/3f4kp-f9653
This paper formalizes the problem of designing optimal agendas for voting over finite alternative spaces, when voters are assumed to be "naive," (i.e., they do not vote strategically). The class of agendas considered here is quite broad, and includes, as special cases, such methods as pairwise voting, sequential and elimination procedures, partitioning schemes, and all binary procedures. Given individual preferences over the basic alternative space, and various assumptions about how individuals choose between subsets of alternatives, one can then formalize the problem of designing agendas as a dynamic programming problem and solve for optimal agendas, i.e., agendas having either the highest probability of leading to a given alternative or having the highest expected utility to the agenda setter. Illustrations are given showing how the methods can be applied in specific examples.https://authors.library.caltech.edu/records/3f4kp-f9653Experiments on the Core: Some Disconcerting Results for Majority Rule Voting Games
https://resolver.caltech.edu/CaltechAUTHORS:20171017-144159043
Authors: {'items': [{'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}, {'id': 'Ordeshook-P-C', 'name': {'family': 'Ordeshook', 'given': 'Peter C.'}}]}
Year: 2017
DOI: 10.7907/vxjaz-75n80
In the context of spatial majority voting games, considerable experimental support exists for the core as a solution hypothesis when it exists (c.f. Berl, et al, 1976; Fiorina and Plott, 1978). Some recent experimentation, however, hints at possible problems in a finite alternative setting. Isaac and Plott (1978) report several such experiments in which subjects fail to adopt a core, although their experimental design uses a particular procedure of chairman control that might account for these results. Elsewhere (1979b) we report a series of vote trading experiments in which the core's success rate is less than fifty percent.
In this essay we present some additional experimental evidence to suggest that committee choice in simple majority rule games is not dictated solely by whether or not a Condorcet (core) point exists. We conclude that, in the experimental context of open and free discussion, the performance of the core is affected by the structure of alternative space, and also by the structure of the perceived dominance relation beneath the core in the social ordering.https://authors.library.caltech.edu/records/vxjaz-75n80An Impossibility Theorem for Von Neumann-Morgenstern Solutions
https://resolver.caltech.edu/CaltechAUTHORS:20171017-165532954
Authors: {'items': [{'id': 'Ferejohn-J-A', 'name': {'family': 'Ferejohn', 'given': 'John A.'}}, {'id': 'McKelvey-R-D', 'name': {'family': 'McKelvey', 'given': 'Richard D.'}}]}
Year: 2017
DOI: 10.7907/v65dx-j2z11
Recently two game theoretic interpretations of social choice procedures have been offered. First, Wilson (1970) and Plott, (1974) suggested that, for each environment, the value of a choice function might constitute a "solution" or stable set that could arise from the play of some underlying cooperative game. In this view, and important problem is to determine if and under what conditions a given solution concept (or notion of stability) can, for some game, characterize the behavior of a given social choice function.
Secondly, social choice functions have been interpreted as collections of equilibria of an underlying noncooperative game (see Gibbard (1973), Peleg (1978), Maskin (1977), and Ferejohn and Grether (1979). In this framework, one major problem is to determine for a given equilibrium correspondence of a suitably chosen noncooperative game. A closely related problem is to determine which noncooperative games possess nonempty equilibrium correspondences of various sorts.
In this paper, we pursue a cooperative game-theoretic interpretation of social choice. And in particular we show that, if a social choice function arises as a Von Neumann Morgenstern solution in each environment, then it is essentially oligarchical in exactly the same sense that "core" selecting choice functions are oligarchic. The conditions under which this conclusion is obtained are, in fact, slightly more restrictive than those for the results on core selecting choice functions but are still weak enough that our result applies to almost any commonly occurring voting scale.https://authors.library.caltech.edu/records/v65dx-j2z11