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on Game Theory |
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Issue of 2011‒05‒07
eleven papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Wu, Haoyang |
| Abstract: | Mechanism design, a reverse problem of game theory, is an important branch of economics. Nash implementation is the cornerstone of the theory of mechanism design. The well-known Maskin's theorem describes the sufficient conditions for Nash implementation when the number of agents are at least three. A recent work [H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. International Journal of Quantum Information, 2010 (accepted) http://arxiv.org/abs/1002.4294 ] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Although quantum mechanisms are theoretically feasible, agents cannot benefit from them immediately due to the restriction of current experimental technologies. In this paper, we will go beyond the obstacle of how to realize quantum mechanisms, and propose an algorithmic mechanism which leads to the same results as quantum mechanisms do. Consequently, the sufficent conditions for Nash implementation are amended not only in the quantum world, but also in the real world. |
| Keywords: | Quantum computing; Mechanism design; Nash implementation. |
| JEL: | D71 |
| Date: | 2011–04–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30067&r=gth |
| By: | Pradiptyo, Rimawan; Sasmitasiwi, Banoon; Sahadewo, Gumilang Aryo |
| Abstract: | This paper aims to analyze subjects’ behavior in an experiment on evolutionary process of prisoners’ dilemma game. The experiment has been designed by using sixteen one-shot prisoners’ dilemma games with payoffs perturbation and random matching players under perfect information. The subjects of the experiment were students and staff in Universitas Gadjah Mada, Indonesia. In contrast to previous studies, for instance Selten and Stoecker’s (1986) Cooper’s, et.al (1991, 1996), the majority of the subjects in this experiment tend to choose Nash equilibrium strategy consistently from the first game. The result showed that the proportion of the Nash equilibrium outcome was consistently in the range of 85%-88%, whereas the tacit cooperation or Pareto optimum outcome was about 1%-2%. There were evidence that payoffs perturbation influences players’ decision. In contrast to the previous studies above, the results from this study revealed that the vast majority of the subjects tend to choose the dominant strategy as prescribed in Game Theory. |
| Keywords: | Prisoners' dilemma; experiment; random-matching players; payoffs perturbation; framing effect |
| JEL: | C92 C73 |
| Date: | 2011–02–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30480&r=gth |
| By: | Albert de-Paz; Jesus Marin-Solano; Jorge Navas (Universitat de Barcelona) |
| Abstract: | In the analysis of equilibrium policies in a dierential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative dierential games in which agents dier in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in innite horizon is also discussed. |
| Keywords: | cooperative solutions, dierential games, asymmetric players, resource games, time-inconsistency, heterogeneous discount rates |
| JEL: | C71 Q20 C73 Q30 C61 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:bar:bedcje:2011253&r=gth |
| By: | Nicolas Quérou; Raphael Soubeyran |
| Abstract: | In this paper, we consider a model of multilateral bargaining where homogeneous agents may exert e¤ort before negotiations in order to inuence their chances to become the proposer. E¤ort levels have a permanent effect on the recognition process (persistent recognition). We prove two main results. First, all voting rules are equivalent (that is, they yield the same social cost) when recognition becomes persistent. Secondly, an equilibrium may fail to exist, because players may have more incentives to reduce their e¤ort level (in order to be included in winning coalitions) than to increase it (in order to increase their proposal power). Both results di¤er greatly from the case where recognition is transitory: Yildirim (2007) shows that una- nimity is the unique strictly optimal rule, and that an equilibrium always exists (under mild assumptions) in such a setting. Moreover, our second conclusion is quite di¤erent from the one obtained in most of the existing literature on bargaining (which assumes an exogenous recognition process), where it is generally considered that it is always in an agents best interest to have a proposal power as high as possible. |
| Date: | 2011–01 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:11-04&r=gth |
| By: | Pierre Courtois; Rabia Nessah; Tarik Tazdaït |
| Abstract: | Social interactions regularly lead to mutually beneficial transactions that are sometimes puzzling. The prisoner’s dilemma and the chicken and trust games prove to be less perplexing than Nash equilibrium predicts. Moral preferences seem to complement self-oriented motivations and their relative predominance in games is found to vary according to the individuals, their environment, and the game. This paper examines the appropriateness of Berge equilibrium to study several 2×2 game situations, notably cooperative games where mutual support yields socially better outcomes. We consider the Berge behavior rule complementarily to Nash: individuals play one behavior rule or another, depending on the game situation. We then define non-cooperative Berge equilibrium, discuss what it means to play in this fashion, and argue why individuals may choose to do so. Finally, we discuss the relationship between Nash and Berge notions and analyze the rationale of individuals playing in a situational perspective. |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:11-05&r=gth |
| By: | Cédric Wanko |
| Abstract: | We define the reversion protocol of a voluntarily implementable Bayesian mechanism in which risk-averse players have no incentive to cheat or to deviate from the mediator’s recommendation and that can greatly improve their equilibrium expected payoffs as compared to those generated through coordination applied to the results of an unsatisfactory mediation. |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:10-11&r=gth |
| By: | Nicolas Quérou; Raphael Soubeyran |
| Abstract: | In this paper, we study the (symmetric) equilibria of a model of multilateral bar- gaining where players are heterogeneous regarding their time preferences, and make costly efforts at the beginning of the process in order to inuence their probabilities of being the proposer for all stages of the negotiation process. We analyse whether the optimality of the unanimity rule (as the voting rule minimizing the social cost resulting from the agents' willingness to buy inuence) characterised in Yildirim (2007) extends to the present situation. In the case of weakly heterogeneous agents, we show that k-majority rules may actually become strictly optimal. Then we provide numerical ex- amples that suggest that there are situations where each type of voting rule (unanimity and strict k-majority) may be socially optimal. |
| Date: | 2010–10 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:10-14&r=gth |
| By: | Herves-Beloso, Carlos; Meo, Claudia; Moreno Garcia, Emma |
| Abstract: | In a scenario with a continuum of asymmetrically informed agents, we analyze how the initial information of a trader may be altered when she becomes a member of a coalition. In contrast to a perfect competition frame, we first show that neither arbitrarily small coalitions nor large coalitions are enough to block an allocation which is not in the core, due to the market failure produced by asymmetric information. However, under mild assumptions, we extend the characterizations of the core provided by Vind and Schmeidler (1972) to economies with asymmetrically informed traders. We then focus on information sharing rules based on the coalitions' size. Assuming the existence of coalitions to which the sharing rule associates an information finer than all the others, we show that the corresponding cores coincide with the one defined by this finest information. Finally, characterizations for the weak fine, the fine and the private core are obtained as particular cases of this equivalence theorem. |
| Keywords: | Coalitions; asymmetric information economies; information sharing; blocking mechanisms; core. |
| JEL: | D71 C02 D82 D51 |
| Date: | 2011–03–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30258&r=gth |
| By: | Pierre Courtois; Tarik Tazdaït |
| Abstract: | What if living in a relatively trustworthy society was sufficient to blindly trust strangers? In this paper we interpret generalized trust as a learning process and analyse the trust game paradox in light of the replicator dynamics. Given that trust inevitably implies doubts about others, we assume incomplete information and study the dynamics of trust in buyer-supplier purchase transactions. Considering a world made of “good” and “bad” suppliers, we show that the trust game admits a unique evolutionarily stable strategy: buyers may trust strangers if, on the whole, it is not too risky to do so. Examining the situation where some players may play, either as trustor or as trustee, we show that this result is robust. |
| Date: | 2011–02 |
| URL: | http://d.repec.org/n?u=RePEc:lam:wpaper:11-06&r=gth |
| By: | Rosa-García, Alfonso; Kiss, Hubert Janos |
| Abstract: | We study a coordination problem where agents act sequentially. Agents are embedded in an observation network that allows them to observe the actions of their neighbors. We find that coordination failures do not occur if there exists a sufficiently large clique. Its existence is necessary and sufficient when agents are homogenous and sufficient when agents differ and their types are private. Other structures guarantee coordination when agents decide in some particular sequences or for particular payoffs. The coordination problem embodied in our game is applied to the problems of revolts and bank runs. |
| Keywords: | social networks; coordination failures; multiple equilibria; revolts; bank runs |
| JEL: | D82 D85 C72 |
| Date: | 2011–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30463&r=gth |
| By: | Schipper, Burkhard C |
| Abstract: | Morris (1996, 1997) introduced preference-based definitions of knowledge of belief in standard state-space structures. This paper extends this preference-based approach to unawareness structures (Heifetz, Meier, and Schipper, 2006, 2008). By defining unawareness and knowledge in terms of preferences over acts in unawareness structures and showing their equivalence to the epistemic notions of unawareness and knowledge, we try to build a bridge between decision theory and epistemic logic. Unawareness of an event is behaviorally characterized as the event being null and its negation being null. |
| Keywords: | unawareness; awareness; knowledge; preferences; subjective expected utility theory; decision theory; null event |
| JEL: | C70 D82 D80 C72 |
| Date: | 2011–04–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30221&r=gth |