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on Game Theory |
| By: | Rene Saran; Roberto Serrano |
| Abstract: | In contexts in which players have no priors, we analyze a learning pro- cess based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are ran- domly matched to play the game (random matching). The relevant long run predictions are minimal sets that are closed under “the same or better reply” operations. Under additional assumptions in each case, the prediction boils down to pure Nash equilibria, pure ex-post equilibria or pure minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in second-price auctions, first-price auctions and Bertrand duopolies. |
| Keywords: | Fixed and Random Matching; Incomplete Information; Ex-Post Regret Learning; Nash Equilibrium; Ex-Post Equilibrium; Minimax Regret |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-11&r=gth |
| By: | Rene Saran; Roberto Serrano |
| Abstract: | We consider the regret matching process with finite memory. For general games in normal form, it is shown that any recurrent class of the dynamics must be such that the action profiles that appear in it constitute a closed set under the “same or better reply” correspondence (CUSOBR set) that does not contain a smaller product set that is closed under “same or better replies,” i.e., a smaller PCUSOBR set. Two characterizations of the recurrent classes are offered. First, for the class of weakly acyclic games under better replies, each recurrent class is monomorphic and corresponds to each pure Nash equilibrium. Second, for a modified process with random sampling, if the sample size is sufficiently small with respect to the memory bound, the recurrent classes consist of action profiles that are minimal PCUSOBR sets. Our results are used in a robust example that shows that the limiting empirical distribution of play can be arbitrarily far from correlated equilibria for any large but finite choice of the memory bound. |
| Keywords: | Regret Matching; Nash Equilibria; Closed Sets under Same or Better Replies; Correlated Equilibria. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2010-10&r=gth |
| By: | Timothy N. Cason; Roman M. Sheremeta; Jingjing Zhang |
| Abstract: | Costless pre-play communication has been found to effectively facilitate coordination and enhance efficiency in games with Pareto-ranked equilibria. We report an experiment in which two groups compete in a weakest-link contest by expending costly efforts. Allowing intra-group communication leads to more aggressive competition and greater coordination than control treatments without any communication. On the other hand, allowing inter-group communication leads to less destructive competition. As a result, intra-group communication decreases while inter-group communication increases payoffs. Our experiment thus provides evidence that communication can either reduce or increase efficiency in competitive coordination games depending on different communication boundaries. This contrasts sharply with experimental findings from public goods and other coordination games, where communication always enhances efficiency and often leads to socially optimal outcomes. |
| Keywords: | Contest, between-group competition, within-group competition, cooperation, coordination, free-riding, experiments |
| JEL: | C70 D72 H41 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:505&r=gth |
| By: | Antonio Romero-Medina; Matteo Triossi |
| Abstract: | This paper presents a sequential admission mechanism where students are allowed to send multiple applications to colleges and colleges sequentially decide the applicants to enroll. The irreversibility of agents decisions and the sequential structure of the enrollments make truthful behavior a dominant strategy for colleges. Due to these features, the mechanism implements the set of stable matchings in Subgame Perfect Nash equilibrium. We extend the analysis to a mechanism where colleges make proposals to potential students and students decide sequentially. We show that this mechanism implements the stable set as well. |
| Keywords: | Stable matching, Subgame perfect Nash equilibrium |
| JEL: | C78 D78 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we1018&r=gth |
| By: | Javier Arin (UPV/EHU) |
| Abstract: | We introduce two new monotonicity properties for core concepts: single-valued solution concepts that always select a core allocation whenever the game is balanced (has a nonempty core). We present one reult of impossibility for one of the properties and we pose several open questions for the second property. The open questions arise because the most important core concepts (the nucleolus and the per capita nucleolus) do not satisfy the property even in the class of convex games. |
| Keywords: | Monotonicity, Core, TU games, nucleolus per capita |
| Date: | 2010–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:201044&r=gth |
| By: | Pálvölgyi Dénes; Peters Hans; Vermeulen Dries (METEOR) |
| Abstract: | The classical bankruptcy problem (O''Neill, 1982) is extended by assuming that the agents have non-homogenous preferences over several estates. A special case is the one in which there are finitely many estates and the agents have homogenous preferences, i.e., constant utilities, per estate. In the general case, i.e., the infinite estate problem, players have arbitrary preferences over an interval of real numbers each of which is regarded as anestate. A strategic game is formulated in which each agent/player distributes his legal entitlement over the estates, resulting in individual claims per estate: each estate is then divided proportionally according to these individual claims. The focus of the paper is on the study of Nash equilibria, in particular on their existence, in finite and infinite estate games. It is also shown that, generally speaking, Nash equilibria are not unique nor Pareto optimal but that they are Pareto optimal in a second best sense: they do not Pareto dominate each other. The paper concludes with a brief consideration of envy-freeness. |
| Keywords: | microeconomics ; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010036&r=gth |
| By: | Breitmoser, Yves |
| Abstract: | In the proto-coalition model of government formation, formateur F appoints a proto-coalition and asks its members whether to start negotiating a coalition contract. If all accept, then the proto-coalition forms and starts negotiating; otherwise a caretaker government assumes office. I extend this model by allowing F to revise the chosen proto-coalition after rejections, that he states pre-conditions for the subsequent negotiations, and that F's opponents may publicly pre-commit to accept/reject certain proposals. The set of equilibrium outcomes is identified as the core if F's opponents can pre-commit and as the convex hull of the core if they cannot pre-commit credibly. This extended model eliminates two flaws of the standard model: it explains why F cannot always install his favored coalition (whatever the status quo) and why "important" coalition members may have more bargaining power in the subsequent negotiations than others. |
| Keywords: | coalition formation; non-cooperative bargaining; core |
| JEL: | C78 D72 C72 |
| Date: | 2010–09–14 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24995&r=gth |
| By: | Berger André; Müller Rudolf; Naeemi Seyed Hossein (METEOR) |
| Abstract: | We study the role of monotonicity in the characterization of incentive compatible allocation rules when types are multi-dimensional, the mechanism designer may use monetary transfers, and agents have quasi-linear preferences over outcomes and transfers. It is well-known that monotonicity of the allocation rule is necessary for incentive compatibility. Furthermore, if valuations for outcomes are either convex or differentiable functions in types, revenue equivalence literature tells that path-integrals of particular vector fields are path-independent. For the special case of linear valuations it is known that monotonicity plus path-independence is sufficient for implementation. We show by example that this is not true for convex or differentiable valuations, and introduce a stronger version of monotonicity, called path-monotonicity. We show that path-monotonicity and path-independence characterize implementable allocation rules if (1) valuations are convex and type spaces are convex; (2) valuations are differentiable and type spaces are path-connected. Next we analyze conditions under which monotonicity is equivalent to path-monotonicity. We show that an increasing difference property of valuations ensures this equivalence. Next, we show that for simply connected type spaces incentive compatibility of the allocation rule is equivalent to path-monotonicity plus incentive compatibility in some neighborhood of each type. This result is used to show that on simply connected type spaces incentive compatible allocation rules with a finite range are completely characterized by path--monotonicity, and thus by monotonicity in cases where path-monotonicity and monotonicity are equivalent. This generalizes a theorem by Saks and Yu to a wide range of settings. |
| Keywords: | microeconomics ; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010035&r=gth |
| By: | Dino Gerardi; Johannes Horner; Lucas Maestri |
| Abstract: | We examine the buyer-seller problem under different levels of commitment. The seller is informed of the quality of the good, which affects both his cost and the buyer's valuation, but the buyer is not. We characterize the allocations that can be achieved through mechanisms in which, unlike with full commitment, the buyer has the option to "walk away" after observing a given offer. We further characterize the equilibrium payoffs that can be achieved in the bargaining game in which the seller makes all the offers, as the discount factor goes to one. This allows us to identify how different levels of commitment affect outcomes, and which constraints, if any, preclude efficiency. |
| Keywords: | bargaining; mechanism design; market for lemons |
| JEL: | C70 C78 D82 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:151&r=gth |
| By: | Schumacher, Heiner; Hadnes, Myriam |
| Abstract: | We propose a theory that explains why rational agents start to believe in a causal relationship between unrelated events. Agents send and collect messages through a communication network. If they are convinced of a relationship between two events, they send messages confirming their belief with higher probability than messages contradicting it. The network aggregates this communication bias over individuals. Therefore, agents may find a strong relationship between unrelated events even if the communication bias is very small. We apply this model to an informal economy where the fear of punishment by supernatural forces prevents agents from cheating others. -- |
| Keywords: | Informal Contract Enforcement,Communication,Learning,Networks |
| JEL: | C72 L14 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:gdec10:11&r=gth |
| By: | Alexey Kushnir |
| Abstract: | Some labor markets have recently developed formal signaling mechanisms, e.g. the signaling for interviews in the job market for new Ph.D. economists. We evaluate the effect of such mechanisms on two-sided matching markets by considering a game of incomplete information between firms and workers. Workers have almost aligned preferences over firms: each worker has 'typical' commonly known preferences with probability close to one and 'atypical' idiosyncratic preferences with the complementary probability close to zero. Firms have commonly known preferences over workers. We show that the introduction of a signaling mechanism is harmful for this environment. Though signals transmit previously unavailable information, they also facilitate information asymmetry that leads to coordination failures. As a result, the introduction of a signaling mechanism lessens the expected number of matches when signals are informative. |
| Keywords: | Signaling, cheaptalk, matching |
| JEL: | C72 C78 D80 J44 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:509&r=gth |