|
on Game Theory |
|
Issue of 2009‒02‒14
fourteen papers chosen by Laszlo A. Koczy Budapest Tech and Maastricht University |
| By: | Evan Shellshear (Institute of Mathematical Economics, Bielefeld University) |
| Abstract: | This paper investigates core stability of cooperative, TU games via a fuzzy extension of the totally balanced cover of a TU game. The stability of the core of the fuzzy extension of a game, the concave extension, is shown to reflect the core stability of the original game and vice versa. Stability of the core is then shown to be equivalent to the existence of an equilibrium of a certain correspondence. |
| Keywords: | cooperative game, core, stable set, fuzzy coalition, fuzzy game, core stability |
| JEL: | C71 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:410&r=gth |
| By: | John Duffy; Jack Ochs |
| Abstract: | We experimentally examine equilibrium selection concepts in static and dynamic binary choice games of complete information with strategic complementarities known as “entry” games. Examples include speculative attacks, bank runs and refinancing decisions by multiple lenders. We explore behavior when the value of a state variable is known to all players in advance of making their action choices. Such games give rise to multiple equilibria and coordination problems. Our specific aim is to assess the predictive power of two different equilibrium selection principles. In static entry games, we test the theory of global games as an equilibrium selection device. This theory posits that players play games of complete information as if they were playing a related global game of incomplete information. In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs it is irreversible. The number of people who have already entered is part of the state description, and individuals can condition their decisions on that information. If the state variable does not indicate that entry is dominated, the efficient subgame perfect equilibrium prediction calls for all players to immediately choose to enter, thereby resolving the coordination problem. This subgame perfect entry threshold in the dynamic game will generically differ from the global game threshold in static versions of the same entry game. Our experimental findings suggest that entry thresholds in both static and dynamic versions of the same entry game are surprisingly similar. The mean entry threshold in the static game lies below the global game equilibrium threshold while the mean entry threshold in the dynamic game lies above the efficient subgame perfect equilibrium threshold. An important implication of this finding is that if one were to observe only the value of the state variable and the number of people who enter by the end of the game one could not determine whether the static or the dynamic game had been played. |
| JEL: | C72 C73 D82 D83 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:pit:wpaper:376&r=gth |
| By: | Alessandro Pavan; Giacomo Calzolari |
| Abstract: | This paper considers games in which multiple principals contract simultaneously with the same agent. We introduce a new class of revelation mechanisms that, although it does not always permit a complete equilibrium characterization, it facilitates the characterization of the equilibrium outcomes that are typically of interest in applications (those sustained by pure-strategy profiles in which the agent's behavior in each relationship is Markov, i.e., it depends only on payoff-relevant information such as the agent's type and the decisions he is inducing with the other principals). We then illustrate how these mechanisms can be put to work in environments such as menu auctions, competition in nonlinear tariffs, and moral hazard settings. Lastly, we show how one can enrich the revelation mechanisms, albeit at a cost of an increase in complexity, to characterize also equilibrium outcomes sustained by non-Markov strategies and/or mixed-strategy profiles. |
| Keywords: | Mechanism design, contracts, revelation principle, menus, endogenous payoff-relevant information |
| JEL: | D89 C72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:85&r=gth |
| By: | Stefano Demichelis; Jean-Jacques Herings; Dries Vermeulen |
| Abstract: | We define an algebro-topological concept of essential map and we use it to prove several results in the theory of general equilibrium and nash equilibrium refinement. |
| Keywords: | fixed point theory, game theory, equilibrium theory, stability of Nash equilibrium, multiplicity of equilibria |
| JEL: | C72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:94&r=gth |
| By: | Naoki Yoshihara |
| Abstract: | In this paper, we consider political competition games of two parties in multi-dimensional policy spaces, where the two parties have two factions, opportunists and militants, that intra-party bargain with each other. In such a game, we adopt the party-unanimity Nash equilibrium (PUNE) [Roemer (1998; 1999; 2001)] as an appropriate solution concept, and examine the general existence problem of this. In particular, we suppose that any faction of each party does not necessarily have dictatorial power. We then provide a general existence theorem for PUNE in this class of games. |
| Keywords: | multi-dimensional political competition games, partyunanimity Nash equilibria, pure-compromise PUNE |
| JEL: | M12 M5 J31 J33 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:a511&r=gth |
| By: | Claus-Jochen Haake (Institute of Mathematical Economics, Bielefeld University); Bettina Klaus (Baker Library, Harvard Business School) |
| Abstract: | We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable. |
| Keywords: | matching with couples, (Maskin) monotonicity, Nash implementation, stability, weakly responsive preferences |
| JEL: | C62 C78 D78 J41 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:399&r=gth |
| By: | Luca Anderlini; Dino Gerardi; Roger Lagunoff |
| Abstract: | We study strategic information transmission in an organization consisting of an infinite sequence of individual decision makers. Each decision maker chooses an action and receives an informative but imperfect signal of the once-and-for-all realization of an unobserved state. The state affects all individuals' preferences over present and future decisions. Decision makers do not directly observe the realized signals or actions of their predecessors. Instead, they must rely on cheap-talk messages in order to accumulate information about the state. Each decision maker is therefore both a receiver of information with respect to his decision, and a sender with respect to all future decisions. We show that if preferences are not perfectly aligned "full learning" equilibria - ones in which the individuals' posterior beliefs eventually place full weight on the true state - do not exist. This is so both in the case of private communication, in which each individual only hears the message of his immediate predecessor, and in the case of public communication, in which a decision maker hears the message of all his predecessors. Surprisingly, in the latter case full learning may be impossible even in the limit as all members of the organization become infinitely patient. We also consider the case where all individuals have access to a mediator who can work across time periods arbitrarily far apart. In this case full learning equilibria exist. |
| Keywords: | Communication, Learning, Dynamic Strategic Information Transmission |
| JEL: | C70 C72 C73 D80 D83 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:82&r=gth |
| By: | Joachim Rosenmüller (Institute of Mathematical Economics, Bielefeld University); Benyamin Shitovitz (Department of Economics, Haifa University) |
| Abstract: | We characterize convex vNM-Stable Sets according to von Neumann and Morgenstern for orthogonal linear production games with a continuum of players. The results of [Rosenmüller & Shitovitz, International Journal of Game Theory 29 (2000)] are thereby substantially improved. Simultaneously, this is a corrigendum concerning the proof of a lemma in our first paper. |
| Date: | 2008–01 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:396&r=gth |
| By: | Loukas Balafoutas |
| Abstract: | This paper analyses the impact of third party beliefs and payoffs on decision making, in the context of a three person repeated game. Two players can collude and increase their intertemporal payoffs, but doing so generates an externality for an inactive player (third party). The model assumes that some players are guilt averse and conditions their emotional responses on the perceived beliefs of the third party; this leads to a self-fulfilling mechanism, where beliefs tend to be confirmed through their impact on psychological payoffs. The experimental findings reveal that the third party’s beliefs are the dominant factor driving behaviour. On the contrary, third party payoffs do not seem to matter. These results are in line with the predictions of psychological game theory, extending them to third parties. Moreover, they give some insights on the relevant weight of different theories (social preferences, reciprocity, guilt) in the shaping of pro-social behaviour. |
| Keywords: | psychological games, guilt, third party, corruption |
| JEL: | C73 C91 D73 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2009-01&r=gth |
| By: | Jihong Lee (Birkbeck College, University of London); Qingmin Liu (Department of Economics, University of Pennsylvania) |
| Abstract: | In many real world negotiations, from wage contract bargaining to product liability disputes, the bargaining parties often interact repeatedly and have the option of seeking outside judgement. This paper studies a model of repeated bargaining with a third party to analyze how and why bargaining postures endogenously evolve over time. A privately informed long-lived player bargains with a sequence of short-lived players, one at a time. Should the players fail to reach an agreement, an unbiased yet imperfect third party is called upon to make a judgement. The uninformed short-lived players learn through two channels: observed behavior of the informed player (\soft" information) and, if any, verdicts of the third party (\hard" information). The long-lived player wants to guard his private information by bargaining tough but at the expense of more information disclosure from the third party. As a result of the strategic use of these two sources of information, the players' bargaining postures change as the uninformed players' beliefs evolve. Interestingly, as third party information becomes more precise, the players adopt tough bargaining postures for a wider range of beliefs. Many repeated bargaining problems can be analyzed in this framework. In particular, the equilibrium dynamics provide an explanation for the puzzling contrast between the bargaining postures of Merck and Pfizer in their recent high-profile product liability litigations. The results also help us understand several other phenomena documented in the related literature. |
| Keywords: | bargaining posture, repeated bargaining, third party information, reputation |
| JEL: | C61 C73 C78 D82 |
| Date: | 2008–11–04 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:09-001&r=gth |
| By: | Michele Lombardi; Naoki Yoshihara |
| Abstract: | We provide three alternative characterizations of the proportional solution defined on compact and comprehensive bargaining problems with claims that are not necessarily convex. One characterization result is obtained by using, together with other standard axioms, two solidarity axioms. Another characterization theorem shows that the single-valuedness axiom is dispensable even within the class of nonconvex problems if the standard symmetry axiom is imposed. |
| Keywords: | Bargaining problems, claims point, proportional solution, nonconvexity, solidarity axioms |
| JEL: | C78 D60 D70 |
| Date: | 2008–06 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:a501&r=gth |
| By: | López-Pérez, Raúl (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.) |
| Abstract: | We present a game-theoretical model that accounts for abundant experimental evidence from games with non-binding communication (‘cheap talk’). It is based on two key ideas: People are conditionally averse to break norms of honesty and fairness (i.e., the emotional cost of breaking a norm is low if few people comply), and heterogeneous with regard to their concern for norms. The model explains (a) why cooperation in social dilemmas rises if players can previously announce their intended play, (b) why details of the communication protocol like the number of message senders and the order in which players communicate affect cooperation, (c) why players in sender-receiver games tend to transmit more information than a standard analysis would predict, and (d) why senders of false messages are often sanctioned if punishment is available. |
| Keywords: | Communication; Cooperation; Fairness; Heterogeneity; Honesty; Reciprocity; Social Norms |
| JEL: | C72 D01 D62 D64 Z13 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:uam:wpaper:200901&r=gth |
| By: | Christine Hauser; Hugo Hopenhayn |
| Abstract: | How is cooperation without immediate reciprocity sustained in a long term relationship? We study the case of two players in continuous time who have privately observable opportunities to provide favors, and where the arrival of these opportunities is a Poisson process. Favors provided by a player give her an entitlement to future favors from her partner. As opposed to a "chips mechanism" where the rate of exchange of favors is one, we allow for two features: first, for the rate of exchange to depend on current entitlements, and second, for the possibility of depreciation or appreciation of entitlements. We show that these two features allow for considerably higher payoffs. We characterize and solve for the Pareto frontier of Public Perfect Equilibria (PPE) and show that it is self-generating. This guarantees that the equilibrium is renegotiation proof. We also find that optimal PPE have two key characteristics: 1) the relative price of favors decreases with a player's entitlement and 2) the disadvantaged player's utility increases over time during periods of no trade, so in the optimal equilibria there is forgiveness. |
| Keywords: | repeated games, jump process, continuous time |
| JEL: | C73 C63 D81 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:88&r=gth |
| By: | Christine Hauser |
| Abstract: | This paper studies the provision of a public good between two agents under lack of commitment and applies it to the problem of children's consumption in separated couples, where children are considered to be public goods. The custodial mother controls the child's consumption, whereas the father can contribute indirectly by making monetary transfers to the mother, but has no control over how the mother spends them. Using minmax punishments, I look for the Pareto frontier of the Subgame Perfect Equilibrium payoffs, and characterize the equilibrium and long term implications of the model. As in the previous literature, agents' consumptions and continuation values covary positively with their income levels. In the case where the constraint for the public good provision binds, both agents' private consumptions increase relative to the public good provision. In the long run, if some first best allocation is sustainable, the long-term equilibrium will converge to a first best allocation. Otherwise, agents' utilities oscillate over a finite set of values. I then study the theoretical implications of one-sided enforcement when the public good provider has the authority to enforce transfers from the second agent. This is motivated by the wave of US policy reforms to enforce child support payments from fathers. The model predicts an increase in the ratio of the mother's consumption to the child's. |
| Keywords: | insurance, lack of commitment, optimal dynamic contract, public good |
| JEL: | C72 C73 D90 E21 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:87&r=gth |