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on Game Theory |
| By: | Sutter, Matthias (Department of Economics, School of Business, Economics and Law, Göteborg University); Czermak, Simon (Department of Public Finance, University of Innsbruck); Feri, Francesco (Department of Public Finance, University of Innsbruck) |
| Abstract: | We present an experiment on strategic thinking and behavior of individuals and teams in oneshot normal-form games. Besides making choices, decision makers have to state their firstand second-order beliefs. We find that teams play the Nash strategy significantly more often, and their choices are more often consistent by being a best reply to first order beliefs. We identify the complexity of a game and the payoffs in equilibrium as determining the likelihood of consistent behavior according to textbook rationality. Using a mixture model, the estimated probability to play strategically is 62% for teams, but only 40% for individuals.<p> |
| Keywords: | Strategic sophistication; beliefs; experiment; team decision making; individual decision making |
| JEL: | C72 C91 C92 |
| Date: | 2010–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:gunwpe:0430&r=gth |
| By: | Yakov Babichenko |
| Abstract: | A completely uncoupled dynamic is a repeated play of a game, where each period every player knows only his action set and the history of his own past actions and payoffs. One main result is that there exist no completely uncoupled dynamics with finite memory that lead to pure Nash equilibria (PNE) in almost all games possessing pure Nash equilibria. By "leading to PNE" we mean that the frequency of time periods at which some PNE is played converges to 1 almost surely. Another main result is that this is not the case when PNE is replaced by "Nash epsilon-equilibria": we exhibit a completely uncoupled dynamic with finite memory such that from some time on a Nash epsion-equilibrium is played almost surely. |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp529&r=gth |
| By: | Miettinen, Topi (Stockholm Institute of Transition Economics); Perea, Andrés (Maastricht University, Department of Quantitative Economics) |
| Abstract: | We extend the Ståhl-Rubinstein alternating-offer bargaining procedure to allow players, prior to each bargaining round, to simultaneously and visibly commit to some share of the pie. If commitment costs are small but increasing in the committed share, then the unique outcome consistent with common belief in future rationality (Perea, 2009), or more restrictively subgame perfect Nash equilibrium, exhibits a second mover advantage. In particular, as the smallest share of the pie approaches zero, the horizon approaches in…nity, and commitment costs approach zero, the unique bargaining outcome corresponds to the reversed Rubinstein outcome (d/(1 + d); 1/(1 + d)). |
| Keywords: | alternating offer bargaining; bargaining power; commitment; epistemic game theory; patience |
| JEL: | C72 C78 D84 |
| Date: | 2009–11–17 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hasite:0008&r=gth |
| By: | Walter Trockel (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two person bargaining games. Based on an approximate foundation due to Myerson (1997) for any two-person bargaining game (S, d) an extensive form game G^{S,d} is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game. By a modification of G^{S,d} the analogous result is provided for subgame perfect equilibria. Finally, it is indicated how these results can be extended to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium. |
| Keywords: | Raiffa solution, non-cooperative foundation Nash program, implementation, solution based social choice rule |
| JEL: | C71 C72 C78 |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:426&r=gth |
| By: | Walter Trockel (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | This paper provides four axioms that uniquely characterize the Sequential Raiffa solution proposed by Raiffa (1951, 1953) for two-person bargaining games. Three of these axioms are standard and are shared by several popular bargaining solutions. They suffice to characterize these solutions on TU-bargaining games where they coincide. The fourth axiom is a weakening of Kalai's (1977) axiom of step-by-step negotiating and turns out to be sort of a dual condition to a weaker version of Nash's IIA-axiom that together with the three standard axioms suffices to characterize the Nash bargaining solution due to Nash (1950). A conclusion of this axiomatization is that in contrast to all other known bargaining solutions the Sequential Raiffa solution does not represent just another kind of fairness or equity condition in addition to the three standard axioms but rather is determined by indefinite repeated application of the three standard axioms. |
| Keywords: | bargaining games, Raiffa solution, Nash solution, axiomatization |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:425&r=gth |
| By: | Gary Bornstein; Ori Weisel |
| Abstract: | Explaining human cooperation in large groups of non-kin is a major challenge to both rational choice theory and the theory of evolution. Recent research suggests that group cooperation can be explained assuming that cooperators can punish non-cooperators or cheaters. The experimental evidence comes from economic games in which group members are informed about the behavior of all others and cheating occurs in full view. We demonstrate that under more realistic information conditions, where cheating is less obvious, punishment is ineffective in enforcing cooperation. Evidently, the explanatory power of punishment is constrained by the visibility of cheating. |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp528&r=gth |
| By: | Costa-Gomes, Miguel A. (University of Aberdeen); Huck, Steffen (University College London); Weizsäcker, Georg (University College London) |
| Abstract: | In many economic contexts, an elusive variable of interest is the agent's expectation about relevant events, e.g. about other agents' behavior. Recent experimental studies as well as surveys have asked participants to state their beliefs explicitly, but little is known about the causal relation between beliefs and other behavioral variables. This paper discusses the possibility of creating exogenous instrumental variables for belief statements, by shifting the probabilities of the relevant events. We conduct trust game experiments where the amount sent back by the second player (trustee) is exogenously varied by a random process, in a way that informs only the first player (trustor) about the realized variation. The procedure allows detecting causal links from beliefs to actions under plausible assumptions. The IV estimates indicate a significant causal effect, comparable to the connection between beliefs and actions that is suggested by OLS analyses. |
| Keywords: | social capital, trust game, instrumental variables, belief elicitation |
| JEL: | C72 C81 C91 D84 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp4709&r=gth |
| By: | Dror Lellouche; Assaf Romm |
| Abstract: | Should an auctioneer start a rising auction from some starting price or set it as a reservation price? Under what circumstances might a bidder find it rational to raise the current offer by a substantial factor instead of making just a small increase above the highest bid? This paper aims to answer both of these questions by exploring the implications of jump bidding over the information sets available to the bidders. Our motivation is to find whether hiding the information about other players' signals might be beneficial for one of the bidders. We first show that it is better for the auctioneer to set a reservation price rather than "jump" to the starting price. We then prove that in a very general setting and when bidders are risk-neutral there exist no equilibrium with jump bidding (in non-weakly dominated strategies). Finally, we demonstrate that jump bidding might be a rational consequence of risk aversion, and analyze the different effects at work. |
| Date: | 2009–12 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp526&r=gth |
| By: | Miettinen, Topi (Stockholm Institute of Transition Economics) |
| Abstract: | This paper introduces the payoff-confirming analogy-based expectation equilibrium (PCABEE) as a way to refine the set of analogy-based equilibria and the associated admissible analogy partitions. In addition to the actions of others, own payoff history provides information about others’ strategies but, yet, non-Bayesian Nash equilibria may exist both with an incorrect and a correct prior. We provide general conditions when this happens. Two stylized employer-employee interactions, one with a correct and one with an incorrect prior, are provided illustrating how PCABEE can be used to analyze robust stereotypes and how incorrect such stereotypes may lead to discrimination. |
| Keywords: | analogy expectations; bounded rationality; curse; learning; discrimination; stereotypes |
| JEL: | C72 D82 |
| Date: | 2009–12–28 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hasite:0007&r=gth |
| By: | Marc Fleurbaey; John Roemer |
| Date: | 2010–02–01 |
| URL: | http://d.repec.org/n?u=RePEc:cla:najeco:814577000000000442&r=gth |
| By: | Ziv Hellman; Dov Samet |
| Abstract: | To answer the question in the title we vary agents' beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agent's knowledge results in an increase in common knowledge. We show that for partition profiles which are tight the set of consistent type profiles is topologically large, while for partition profiles which are not tight this set is topologically small. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp532&r=gth |
| By: | Sergiu Hart |
| Abstract: | Stochastic dominance is a partial order on risky assets (“gamblesâ€) that is based on the uniform preference, of all decision-makers (in an appropriate class), for one gamble over another. We modify this, first, by taking into account the status quo (given by the current wealth) and the possibility of rejecting gambles, and second, by comparing rejections that are substantive (that is, uniform over wealth levels or over utilities). This yields two new stochastic orders: wealth-uniform dominance and utility-uniform dominance. Unlike stochastic dominance, these two orders are complete: any two gambles can be compared. Moreover, they are equivalent to the orders induced by, respectively, the Aumann–Serrano (2008) index of riskiness and the Foster–Hart (2009a) measure of riskiness. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp531&r=gth |
| By: | Kris De Jaegher |
| Abstract: | This paper develops a model of supplier-induced demand as strategic framing where the patient has reference-dependent references, and the physician can persuade the patient to buy a treatment by affecting the patient.s reference point. In the main result, the patient is assumed to have a constant rate of risk aversion (lovingness) in the gain (loss) region. Two scenarios are treated. In the cure scenario, the physician wants to frame the patient.s decision problem such that he prefers to buy a risky curative treatment rather than no treatment. It is shown that the physician is most persuasive if she sets a high reference point, such that the patient sees all payoffs as losses down from that reference point. In the prevention scenario, the physician wants to frame the patient.s decision problem such that he prefers a safe preventive treatment rather than no treatment. In this case, the physician.s optimal framing either involves framing all payoffs as gains, thus making the patient riskaverse. Alternatively, loss aversion is exploited by framing only the fact of getting ill (rather than having prevented illness) as a loss. |
| Keywords: | supplier-induced demand, prospect theory, strategic framing |
| JEL: | D82 I11 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:1001&r=gth |
| By: | Josef Hofbauer (Department of Mathematics, University of Vienna - Universität Wien); Sylvain Sorin (EC - Equipe de Combinatoire - CNRS : UMR7090 - Université Pierre et Marie Curie - Paris VI, Department of Economics, Ecole Polytechnique - CNRS : UMR7176 - Polytechnique - X); Yannick Viossat (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris Dauphine - Paris IX) |
| Abstract: | Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics. |
| Keywords: | replicator dynamics; best reply dynamics; logit map; perturbed differential inclusion; internally chain transitive set; attractor |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-00360767_v1&r=gth |
| By: | Evrenk, Haldun (Suffolk University, Economics) |
| Abstract: | I study both local and global Nash equilibria of a model of three-candidate unidimensional spatial competition. In the model, candidates may have different non-policy characteristics (valence). Generalizing the base model studied in Evrenk (2009a;b) the model allows for an asymmetric voter density as well as plurality-maximizing candidates. Unlike the standard Hotelling-Downs model of multi-candidate competition, under an asymmetric density with (heterogenous) vote-maximizing candidates a pure strategy Nash equilibrium (PSNE) exists. Further, this PSNE is free from several non-plausible features of PSNE under a symmetric density. When candidates are plurality-maximizers, some of the PSNE are supported by paradoxical candidate behavior. Further, when voter density is asymmetric and candidates are plurality-maximizers, there are several non-monotonicities in the PSNE. |
| Keywords: | Valence; three-candidate competition; plurality maximization; local Nash equilibrium; asymmetric voter density |
| JEL: | C72 H89 |
| Date: | 2010–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:suf:wpaper:2010-1&r=gth |
| By: | Evrenk, Haldun (Suffolk University, Economics); Kha, Dmitriy (Suffolk University, Economics) |
| Abstract: | We study the effects of stochastic (probabilistic) voting on equilibrium locations, equilibrium vote shares and comparative statics in a setup with three heterogenous candidates and a single-dimensional issue space. Comparing the equilibria with and without stochastic voting, we find that under an appropriate level of uncertainty about voter behavior, the model has a pure strategy Nash Equilibrium (PSNE) that is free from several non-plausible features of the PSNE under deterministic voting. The results are robust to extensions to asymmetric density and plurality maximization. |
| Keywords: | Probabilistic voting; valence; three-candidate competition; centripetal incentives |
| JEL: | C72 H89 |
| Date: | 2010–02–02 |
| URL: | http://d.repec.org/n?u=RePEc:suf:wpaper:2010-2&r=gth |