nep-gth New Economics Papers
on Game Theory
Issue of 2008‒09‒29
twelve papers chosen by
Laszlo A. Koczy
Budapest Tech and Maastricht University

  1. Evolutionary Stability in Common Pool Resources. By Jean-Philippe Atzenhoffer
  2. Stable Many-to-Many Matchings with Contracts By Bettina-Elisabeth Klaus; Markus Walzl
  3. On the vertices of the k-addiive core By Michel Grabisch; Pedro Miranda
  4. Nash Demand Game and the Kalai-Smorodinsky Solution By Nejat Anbarci; John Boyd
  5. A Noncooperative Approach to Bankruptcy Problems with an Endogenous Estate By Karagozoglu Emin
  6. Noncooperative Oligopoly in Markets with a Continuum of Traders By Busetto, Francesca; Codognato, Giulio; Ghosal, Sayantan
  7. An extension of Reny's theorem without quasiconcavity By Philippe Bich
  8. Distributive Concerns in the Bankruptcy Problem with an Endogenous Estate By Karagozoglu Emin
  9. Leadership by Confidence in Teams By Kobayashi, Hajime; Suehiro, Hideo
  10. Questionable Luxury Taxes: Results from a Mating Game By Thomas, Tobias
  11. Strategic behaviour and risk taking in football By Stephen Dobson; John Goddard
  12. Is mistrust self-fulfilling? By Reuben, Ernesto; Sapienza, Paola; Zingales, Luigi

  1. By: Jean-Philippe Atzenhoffer
    Abstract: The Tragedy of the Commons refers to the dissipation of a common- pool ressource when any appropriator has free access to it. Under the behavior of absolute payoff maximisation, the common-pool resource game leads to a Nash equilibrium in which the resource is overexploited. However, some empirical studies show that the overutilization is even larger than the Nash equilibrium predicts. We account for these results in an evolutionary framework. Under an imitation-experimentation dynamics, the long run stable behavior implies a larger exploitation of the resource than in the classical Nash equilibrium.
    Keywords: common-pool resource, imitation behavior, evolutionary stable strategy, evolutionary games.
    JEL: C73 D41 Q20
    Date: 2008
  2. By: Bettina-Elisabeth Klaus (Harvard Business School, Negotiation, Organizations & Markets Unit); Markus Walzl (School of Economics and Management, Free University of Bozen/Bolzano, Italy)
    Abstract: We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting sets of stable allocations for general, substitutable, and strongly substitutable preferences. Apart from obtaining "set inclusion results" on all three domains, we introduce weak setwise stability as a new stability concept and prove that for substitutable preferences the set of pairwise stable matchings is nonempty and coincides with the set of weakly setwise stable matchings. For strongly substitutable preferences the set of pairwise stable matchings coincides with the set of setwise stable matchings.
    Keywords: Many-to-Many Matching, Matching with Contracts, Pairwise Stability, Setwise Stability.
    JEL: C62 C78 D78 J41
    Date: 2007–08
  3. By: Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Pedro Miranda (Universidad Complutense de Madrid - Universidad Complutense de Madrid)
    Abstract: The core of a game $v$ on $N$, which is the set of additive games $\phi$ dominating $v$ such that $\phi(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular functions, matroids and the greedy algorithm. In many cases however, the core is empty, and alternative solutions have to be found. We define the $k$-additive core by replacing additive games by $k$-additive games in the definition of the core, where $k$-additive games are those games whose M\"obius transform vanishes for subsets of more than $k$ elements. For a sufficiently high value of $k$, the $k$-additive core is nonempty, and is a convex closed polyhedron. Our aim is to establish results similar to the classical results of Shapley and Ichiishi on the core of convex games (corresponds to Edmonds' theorem for the greedy algorithm), which characterize the vertices of the core.
    Date: 2008
  4. By: Nejat Anbarci (School of Accounting, Economics and Finance, Deakin University,); John Boyd (Department of Economics, Florida International University)
    Abstract: We introduce two new variations on the Nash demand game. One, like all known Nash-like demand games so far, has the Nash solution outcome as its equilibrium outcome. In the other, the range of solutions depends on an exogenous breakdown probability; surprisingly, the Kalai-Smorodinsky outcome proves to be the most robust equilibrium outcome. While the Kalai-Smorodinsky solution always finishes on top, there is no possible general ranking among the remaining solution concepts considered; in fact, the rest of the solution concepts take their turns at the bottom at various bargaining problems, depending on the specifics of the bargaining setup.
    Keywords: Nash demand game, Kalai-Smorodinsky Solution.
    Date: 2008–09
  5. By: Karagozoglu Emin (METEOR)
    Abstract: We introduce a new class of bankruptcy problems in which the value of the estate is endogenous and depends on agents'' investment decisions. There are two investment alternatives: investing in a company and becoming a shareholder (risky asset) and depositing money into a bank (risk-free asset). Bankruptcy is a possible event only for the risky asset. We define a game between agents each of which aims to maximize his expected payoff by choosing an investment alternative and a company management which aims to maximize the investment in the company by choosing a bankruptcy rule. There are two types of agents in our model, who are differentiated by their incomes. We, first, consider three well-known bankruptcy rules: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that there always exists a pure strategy subgame perfect Nash equilibrium, which involves the proportional rule. This result is independent of the income distribution in the economy and holds even under one-sided uncertainty on the income distribution. We also show that our results can be extended to a larger set of rules containing the Talmud rule along with other rules that belong to the TAL-family. Our results provide, at least, a partial explanation from a strategic point of view for the popular use of the proportional rule in allocating bankrupt companies'' assets to shareholders.
    Keywords: public economics ;
    Date: 2008
  6. By: Busetto, Francesca (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine); Codognato, Giulio (Dipartimento di Scienze Economiche, Universitµa degli Studi di Udine); Ghosal, Sayantan (Department of Economics, University of Warwick)
    Abstract: In this paper, we study three prototypical models of noncooperative oligopoly in markets with a continuum of traders : the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991), the model of Cournot-Nash equilibrium of Lloyd S. Shapley, and the model of Cournot-Walras equilibrium of Busetto et al. (2008). We argue that these models are all distinct and only the Shapley's model with a continuum of traders and atoms gives an endogenous explanation of the perfectly and imperfectly competitive behavior of agents in a one-stage setting. For this model, we prove a theorem of existence of a Cournot-Nash equilibrium.
    JEL: C72 D51
    Date: 2008
  7. By: Philippe Bich (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
    Abstract: In a recent but well known paper, Reny has proved the existence of Nash equilibria for compact and quasiconcave games, with possibly discontinuous payoff functions. In this paper, we prove that the quasiconcavity assumption in Reny's theorem can be weakened: roughly, we introduce a measure allowing to localize the lack of quasiconcavity; this allows to refine the analysis of equilibrium existence
    Keywords: Nash equilibrium, existence, discontinuous games, non quasiconcave
    Date: 2008–09–20
  8. By: Karagozoglu Emin (METEOR)
    Abstract: We compare certain bankruptcy rules in a bankruptcy model with an endogenous estate on the basis of normative criteria. In particular, five properties related to distributive concerns are analyzed: minimal rights first, securement of initial investments, initial investments first, reasonable lower bounds on awards, and reasonable lower bounds on losses. The proportional rule receives the strongest support from this normative analysis among the rules considered. We also observe that the performance of the proportional rule improves in the family of bankruptcy problems with endogenous estates compared to the general set of bankruptcy problems. Our results complement those in Karagozoglu (2008) and provide a broader perspective to bankruptcy problems with endogenous estates.
    Keywords: public economics ;
    Date: 2008
  9. By: Kobayashi, Hajime; Suehiro, Hideo
    Abstract: We study endogenous signaling in teams by analyzing a team production problem with endogenous timing. Each agent of the team is privately endowed with some level of confidence about team productivity. Each of them must then commit a level of effort in one of two periods. At the end of each period, each agent observes his partner's move in this period. Both agents are rewarded by a team output determined by team productivity and total invested effort. Each agent must personally incur the cost of effort that he invested. We show a sufficient condition under which sender and receiver emerge endogenously in a stable equilibrium. This result implies that leadership in teams emerges through the leader's signaling incentives only based on his confidence.
    Keywords: Endogenous Signaling; Team Production; Leadership
    JEL: D82 C72
    Date: 2008–07–07
  10. By: Thomas, Tobias (Helmut Schmidt University, Hamburg)
    Abstract: This contribution provides a game theoretical derivation of market demand as a function of the level and distribution of income in the considered economy: if (i) the price is low, everyone buys the good; if (ii ) the price is high, only the rich buy the good (a status good in a narrow sense). If (iii) the price is located in very high or in middle range, demand collapses. With this, we explain the critical price from which a status good acts as a distinctive signal. In addition, this approach shows the potential welfare-improving impact of conspicuous consumption. Taking these results into account, recommendations by numerous economists to prevent the welfare losses of conspicuous consumption by introducing a luxury tax are highly questionable.
    Keywords: luxury tax; conspicuous consumption; mating model; signaling game; status good
    JEL: C70 D11 D82
    Date: 2008–08
  11. By: Stephen Dobson; John Goddard
    Abstract: This article develops a dynamic game-theoretic model of optimizing strategic behaviour by football teams. Teams choose continuously between defensive and attacking formations and between a non-violent and a violent playing style. Starting from the end of the match and working backwards, the teams’ optimal strategies conditional on the current state of the match are determined by solving a series of two-person non-cooperative subgames. Numerical simulations are used to explore the sensitivity of strategic behaviour to variations in the structural parameters. The model is tested empirically, using English football league data. Teams that are trailing are willing to bear an increased risk of a player dismissal in order to increase the probability of scoring. Teams that are leading or level in scores play cautiously. The scoring rates of teams that are trailing are higher than those of teams that are ahead or level. Stochastic simulations are used to obtain probabilities for match results, conditional upon the state of the match at any stage. The article’s main theoretical and empirical results constitute novel, non-experimental evidence that the strategic behaviour of football teams can be rationalized in accordance with game-theoretic principles of optimizing strategic behaviour by agents when payoffs are uncertain and interdependent.
    Date: 2008–06
  12. By: Reuben, Ernesto; Sapienza, Paola; Zingales, Luigi
    Abstract: We study experimentally the effect of expectations on trustworthiness. Most subjects respond with untrustworthy behavior if they find out that little is expected from them. This suggests that guilt aversion plays an important role in inducing trustworthiness.
    Keywords: trust; trustworthiness; reciprocity; guilt aversion
    JEL: C92 Z13 C72
    Date: 2008–05

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