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on Game Theory |
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Issue of 2009‒10‒24
sixteen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University |
| By: | Andriy Zapechelnyuk (University of Bonn and Kyiv School of Economics) |
| Abstract: | Consider a repeated game where all players follow no-regret strategies by reinforcing the actions that they regret not having played enough in the past. We show that a resulting no-regret dynamic approaches in the long run a best-response dynamic and leads to its invariant sets: rest points (Nash equilibria) or periodic orbits. The convergence results for best-response dynamics known in the literature immediately apply to no-regret dynamics. Thus, every no-regret dynamic leads to Nash equilibrium in zero-sum games, weighted potential and two-player ordinal potential games, supermodular games with diminishing returns, and some other special classes. |
| Keywords: | Regret minimization, no-regret strategy, best-response dynamic, Nash equilibrium, Shapley polygon, curb set |
| JEL: | C44 D81 D83 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:kse:dpaper:21&r=gth |
| By: | Lijue Xie (Centre d'Economie de la Sorbonne); Michel Grabisch (Centre d'Economie de la Sorbonne) |
| Abstract: | In the classical setting of cooperative game theory, it is always assumed that all coalitions are feasible. However in many real situations, there are restrictions on the set of coalitions, for example duo to communication, order or hierarchy on the set of players, etc. There are already many works dealing with games on restricted set of coalitions, defining many different structures for the set of feasible coalitions, called set systems. We propose in this paper to consider k-regular set systems, that is, set systems having all maximal chains of the same length k. This is somehow related to communication graphs. We study in this perspective the core of games defined on k-regular set systems. We show that the core may be unbounded and without vertices in some situations. |
| Keywords: | Cooperative game, feasible coalition, core. |
| JEL: | C71 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09055&r=gth |
| By: | Béal, Sylvain; Rémila, Eric; Solal, Philippe |
| Abstract: | We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings \sl et al. [9] and [10]. The AT solutions are defined with respect to a set, say T, of rooted spanning trees of the communication graph. We characterize these solutions by efficiency, linearity and an axiom of T-hierarchy. Then we prove the following results. Firstly, the AT solution with respect to T is a Harsanyi solution if and only if T is a subset of the set of trees introduced in [10]. Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete. |
| Keywords: | Communication situations ; average tree solution ; Harsanyi solutions ; DFS ; BFS} ; Shapley value ; equal surplus division |
| JEL: | C71 |
| Date: | 2009–09–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17909&r=gth |
| By: | Roberto Serrano (Brown University); Roland Pongou (Brown University) |
| Abstract: | We study the dynamic stability of fidelity networks, which are networks that form in a mating economy of agents of two types (say men and women), where each agent desires direct links with opposite type agents, while engaging in multiple partnerships is considered an act of infidelity. Infidelity is punished more severely for women than for men. We consider two stochastic processes in which agents form and sever links over time based on the reward from doing so, but may also take non-beneficial actions with small probability. In the first process, an agent who invests more time in a relationship makes it stronger and harder to break by his/her partner; in the second, such an agent is perceived as weak. Under the first process, only egalitarian pairwise stable networks (in which all agents have the same number of partners) are visited in the long run, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) are. Next, we apply these results to find that, in the long run, under the first process, HIV/AIDS is equally prevalent among men and women, while under the second, women bear a greater burden. The key message is that anti-female discrimination does not necessarily lead to (weakly) higher HIV/AIDS prevalence among women in the short run, but it does in the long run. |
| Keywords: | Fidelity networks, anti-female discrimination, stochastic stability, HIV/AIDS, union formation models. |
| JEL: | A14 C7 I12 J00 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2009_0909&r=gth |
| By: | Robin P. Cubitt (School of Economics, University of Nottingham); Robert Sugden (School of Economics, University of East Anglia) |
| Abstract: | This paper presents a new iterative procedure for solving finite noncooperative games, the reasoning-based expected utility procedure (RBEU), and compares this with existing iterative procedures. RBEU deletes more strategies than iterated deletion of strictly dominated strategies, while avoiding the conceptual problems associated with iterated deletion of weakly dominated strategies. It uses a sequence of “accumulation” and “deletion” operations to categorise strategies as permissible and impermissible; strategies may remain uncategorised when the procedure halts. RBEU and related “categorisation procedures” can be interpreted as tracking successive steps in players’ own reasoning. |
| JEL: | C72 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2009-16&r=gth |
| By: | Roberto Serrano (Brown University); Yusuke Kamishiro (Brown University) |
| Abstract: | We study information transmission in large interim quasilinear economies using the theory of the core. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We consider independent, ex-post and signal-based replicas of the basic economy. For each, we offer an array of negative and positive convergence results as a function of the complexity of the mechanisms used by coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. Further, all the results are robust to the relaxation of the incentive constraints, and hence suggest a process through which information may get incorporated into a fully revealing equilibrium price function. |
| Keywords: | Core w.r.t. equilibrium blocking, core convergence, independet replicas, ex-mechanisms, mediation, rational expectations equilibrium. |
| JEL: | C71 C72 D51 D82 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2009_0911&r=gth |
| By: | Marek Pycia (UCLA); M. Utku Ünver (Boston College) |
| Abstract: | We study the allocation and exchange of indivisible objects without monetary transfers. In market design literature, some problems that fall in this category are the house allocation problem with and without existing tenants, and the kidney exchange problem. We introduce a new class of direct mechanisms that we call "trading cycles with brokers and owners," and show that (i) each mechanism in the class is coalitional strategy-proof and Pareto-efficient, and (ii) each coalitional strategy-proof and Pareto-efficient direct mechanism is in the class. As corollaries, we obtain new characterizations in the aforementioned market design problems. |
| Keywords: | Mechanism design, coalitional strategy-proofness, Pareto-efficiency, matching, house allocation. |
| JEL: | C78 D78 |
| Date: | 2009–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:715&r=gth |
| By: | Tayfun Sönmez (Boston College); M. Utku Ünver (Boston College) |
| Keywords: | House allocation, kidney exchange, school admissions, market design, lottery mechanisms |
| JEL: | D71 D72 |
| Date: | 2009–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:717&r=gth |
| By: | Wesselbaum, Dennis |
| Abstract: | The efficiency wage theory developed by Akerlof (1982) assumes observability of effort and the ability of firm and worker to commit on their effort/wage decisions. We show that, from a game theoretical point of view, we have to understand the firm/worker relationship as a repeated Prisoner's dilemma. Therefore, cooperation is per se not a (subgame perfect) Nash equilibrium and hence the Akerlof (1982) theory is based upon an implicit assumption of cooperation, which can not be implemented w.l.o.g.. In addition, we find that this approach is a special case of the Shapiro and Stiglitz (1984) approach and hence unify the two approaches. |
| Keywords: | Efficiency Wage; Prisoner's Dilemma; Repeated Game; Subgame Perfect Nash Equilibrium. |
| JEL: | J41 C73 C72 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:18026&r=gth |
| By: | Monique Florenzano (Centre d'Economie de la Sorbonne) |
| Abstract: | This paper is published in Games and Economic Behavior, Vol 66, issue 2, Juillet 2009, pp. 603-605, Special Section in Honor of David Gale. |
| Keywords: | Fixed points, equilibrium, excess demand correspondence, Gale-Nikaido-Debreu lemma, simultaneous optimization approach, Michael selection theorems. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09052&r=gth |
| By: | Pedro, de Mendonça |
| Abstract: | Based on recent proposals on non cooperative dynamic games for analysing climate negotiation outcomes, such as Dutta and Radner (2004, 2006a), we generalize a specific framework for modelling differential games of this type and describe the set of conditions for the existence of closed loop dynamics and its relation to adaptive evolutionary dynamics. We then show that the Dutta and Radner (2004, 2006a) discrete time dynamic setup is a specific case of that generalization and describe the dynamics both analytically and numerically for closed loop feedback and perfect state patterns. Our discussion is completed with the introduction of a cooperative differential framework for welfare analysis purposes, within our non cooperative proposal for climate negotiations. |
| Keywords: | Differential Game Theory; Environmental Economics; Evolutionary Dynamics; Climate Change Treaties |
| JEL: | Q56 C61 C73 C72 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:17889&r=gth |
| By: | Roberto Serrano (Brown University); Rajiv Vohra (Brown University) |
| Abstract: | We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap. |
| Keywords: | Exact implementation, approximate implementation, incomplete information, incentive compatibility, monotonicity. |
| JEL: | C72 D78 D82 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2009_0908&r=gth |
| By: | Daniel Houser; Daniel Schunk; Joachim Winter |
| Abstract: | The role of trust in promoting economic activity and societal development has received considerable academic attention by social scientists. A popular way to measure trust at the individual level is the so-called “investment game” (Berg, Dickhaut, and McCabe, 1995). It has been widely noted, however, that risk attitudes can also affect decisions in this game, and thus in principle confound inferences about trust. We provide novel evidence shedding light on the role of risk attitudes for trusting decisions. To the best of our knowledge our data are the first rigorous evidence that (i) aggregate investment distributions differ significantly between trust and risk environments, and (ii) risk attitudes predict individual investment decisions in risk games but not in the corresponding trust games. Our results are convergent evidence that trust decisions are not tightly connected to a person’s risk attitudes, and they lend support to the “trust” interpretation of decisions in investment games. |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:450&r=gth |
| By: | Roberto Serrano (Brown University) |
| Abstract: | Watson (2007) proposes non-forcing contracts as a way to show the limitations of the mechanism design program with ex-post renegotiation (Maskin and Moore (1999)). If one takes a partial implementation approach, as Watson does, we show that nonforcing contracts do not constitute an intermediate paradigm between implementation with no renegotiation and with ex-post renegotiation. Moreover, taking a full implementation approach, non-forcing contracts fail if and only if one goes outside of the constraints identified by Maskin and Moore, because of the appearance of undesirable equilibria. |
| Keywords: | Contracts, renegotiation, mechanism desing. |
| JEL: | C70 D74 K10 |
| Date: | 2009–09 |
| URL: | http://d.repec.org/n?u=RePEc:cmf:wpaper:wp2009_0907&r=gth |
| By: | Ana Espinola-Arredondo; Felix Munoz-Garcia (School of Economic Sciences, Washington State University) |
| Abstract: | This paper examines countries’ free-riding incentives in international environmental agreements (IEAs) when, first, the treaty is non-enforceable, and second, countries do not have complete information about other countries’ noncompliance cost. We analyze a signaling model whereby the country leading the negotiations of the international agreement can reveal its own noncompliance costs through the commitment level it signs in the IEA. Our results show that countries’ probability to join the IEA is increasing in the free-riding benefits they can obtain from other countries’ compliance, and decreasing in their own noncompliance costs. This paper shows that, when free-riding incentives are strong enough, there is no equilibrium in which all types of countries join the IEA. Despite not joining the IEA, countries invest in clean technologies. Finally, we relate our results with some common observations in international negotiations. |
| Keywords: | Signaling games, environmental agreements, nonbinding negotiations, noncom- pliance cost. |
| JEL: | C72 D62 Q28 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:wsu:wpaper:espinola-5&r=gth |
| By: | Yann Bramoullé; Sanjeev Goyal |
| Abstract: | Favoritism is the act of offering jobs, contracts and resources to members of one's social group in preference to outsiders. Favoritism is widely practiced and this motivates an exploration of its origins and economic consequences. Our main finding is that individuals have an interest to trade favors over time and that this will come at the expense of others, who are outside their group. We show that favoritism is relatively easier to sustain in smaller groups. Favoritism entails social costs as it usually leads to inefficient allocations. However, favoritism can lead to payoff advantages for larger groups. Productivity enhancing investments are larger in groups which practice favoritism. The availability of investment opportunities can reinforce payoff inequalities across groups. |
| Keywords: | Favoritism, nepotism, reciprocity, repeated games |
| JEL: | C73 D71 J71 O10 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:lvl:lacicr:0941&r=gth |