nep-gth New Economics Papers
on Game Theory
Issue of 2013‒06‒30
twelve papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Differential Game with (A)symmetric Players and Heterogeneous Strategies By Benteng Zou
  2. Convergence of best response dynamics in extensive-form games By Xu, Zibo
  3. A concise axiomatization of a Shapley-type value for stochastic coalition processes. By Ulrich Faigle; Michel Grabisch
  4. Modularity and Monotonicity of Games By Takao Asano; Hiroyuki Kojima
  5. Long-Term Relationship Bargaining By Westermark, Andreas
  6. Dominance Solvable Approval Voting Games By Sébastien Courtin; Matias Nùnez
  7. The Role of Incentives in Co-operation Failures By David Bartolini
  8. (Un)stable vertical collusive agreements By Jean J. Gabszewicz; Skerdilajda Zanaj
  9. A positional game for an overlapping generation economy By Ahmad Naimzada; Marina Pireddu
  10. Contracts versus Salaries in Matching: Comment By Jan Christoph Schlegel
  11. Single-Basined Choice By Walter Bossert; Hans Peters
  12. Co-managing common pool resources: Do formal rules have to be adapted to traditional ecological norms? By Björn Vollan; Sebastian Prediger; Markus Frölich

  1. By: Benteng Zou (CREA, Université de Luxembourg)
    Abstract: This paper presents one kind of heterogeneous strategies in some differential games where one player plays open-loop strategy and the other one plays Markovian strategy. On top of the stationary path, this kind of strategies enable the study of trajectory dynamics, even for asymmetric players’ with non-linear-quadratic games.
    Keywords: Differential game, Markovian Nash Equilibrium, Heterogeneous strategy
    JEL: C73 C72
    Date: 2013
  2. By: Xu, Zibo (Dept. of Economic Statistics, Stockholm School of Economics)
    Abstract: We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In a perfect-information game where each player can only move at one node, we prove that all interior approximate best response dynamics converge to the backward induction equilibrium, which is hence the socially stable strategy in the game.
    Keywords: Convergence to Nash equilibrium; games in extensive form; games of perfect information; Nash equilibrium components; best response dynamics; fictitious play; socially stable strategy.
    JEL: C73 D83
    Date: 2013–06–24
  3. By: Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics)
    Abstract: The Shapley value is defined as the average marginal contribution of a player, taken over all possible ways to form the grand coalition N when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general model of coalition formation where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is weaker than the one in the original paper but allows a much more transparent correctness proof. Moreover, the logical independence of the axioms is proved.
    Keywords: Coalitional game, coalition formation process, Shapley value.
    JEL: C71
    Date: 2013–06
  4. By: Takao Asano (Faculty of Economics, Okayama University); Hiroyuki Kojima (Department of Economics, Teikyo University)
    Abstract: The purpose of this paper is twofold. First, we generalize Kajii et al. (2007), and provide a condition under which for a game v, its Mobius inversion is equal to zero within the framework of the k-modularity of v for k >= 2. This condition is more general than that in Kajii et al. (2007). Second, we provide a condition under which for a game v for k >= 2, its Mobius inversion takes non-negative values, and not just zero. This paper relates the study of totally monotone games to that of kmonotone games. Furthermore, the modularity of a game can be related to k-additive capacities proposed by Grabisch (1997). As applications of our results to economics, this paper shows that a Gini index representation of Ben-Porath and Gilboa (1994) can be characterized by using our results directly. Our results can also be applied to potential functions proposed by Hart and Mas-Colell (1989) and further analyzed by Ui et al. (2011). *>= is greater than or equal to.
    Keywords: Belief Functions; Mobius Inversion; Totally Monotone Games; k-additive capacities; Gini Index; Potential Functions
    JEL: C71 D81 D90
    Date: 2013–06
  5. By: Westermark, Andreas (Research Department, Central Bank of Sweden)
    Abstract: We analyze a bargaining model where there is a long-term relationship between a seller and a buyer and there is bargaining over a sequence of surpluses that arrives at fixed points in time. Markov Perfect Equilibria are analyzed and equilibrium payoffs characterized. The transfers between the players can be described as a first-order system of difference equations. Payoffs depend on both current and future surpluses. Future surpluses are important partly because the risk of separation leads to the loss of surplus today and in the future and partly because delay without separation can last into future periods. We also find conditions for existence and uniqueness of equilibria with immediate agreement.
    Keywords: Bargaining; long term relationship
    JEL: C72 C78
    Date: 2013–04–01
  6. By: Sébastien Courtin; Matias Nùnez (Universit´e de Cergy-Pontoise, THEMA, UMR CNRS 8184; Universit´e de Cergy-Pontoise, THEMA, UMR CNRS 8184)
    Abstract: This work provides necessary and sufficient conditions for the dominance solvability of approval voting games. Our conditions are very simple since they are based on the approval relation, a binary relation between the alternatives. We distinguish between two sorts of dominance solvability and prove that the most stringent one leads to the election of the set of CondorcetWinners whereas this need not be the case for the weak version.
    Keywords: Approval voting, Strategic voting, Dominance-solvability, Condorcet Winner
    JEL: C72 D71 D72
    Date: 2013
  7. By: David Bartolini
    Abstract: There are many situations where the best outcome is reached through co-operation and co-ordination of agents’ actions. Although this is the best collective outcome, economic agents may fail to implement such co-operative strategy. The reason for this failure may be lack of information about the gains from co-operation, or lack of capacity to implement the co-operative strategy. The present work focuses on two obstacles to co-operation that are linked with the incentives of the economic agents, and that are present even when the problems of information and capacity are taken care off. The two obstacles are the incentive to free ride and the strategic risk. The former stems from the possibility of obtaining gains without paying the associated costs (which are incurred by the agents that decide to co-operate); the latter is the risk of being the only one (or among the few) that acts co-operatively, so that the agent pays the costs but obtains less than what it would be feasible had other agents decided to co-operate. In this setting, using a game theoretical approach, we distinguish several cases of co-operation failures according to the relevance of those two obstacles. The analysis is then applied to contractual design and financial incentives. The overall message is the importance of identifying the source of co-operation failure in order to devise an effective policy to induce co-operation. It may not be enough to tell people (and institutions) that they should co-operate because it is in their interest, it is necessary to identify the incentives that shape agents’ decisions and are responsible for co-operation failures.
    Keywords: game theory, co-operation and co-ordination failure, economic incentives
    JEL: C70 C72 D86
    Date: 2013–05–27
  8. By: Jean J. Gabszewicz (CORE, Université Catholique de Louvain, Belgique); Skerdilajda Zanaj (CREA, Université de Luxembourg)
    Abstract: In this paper, we extend the concept of stability to vertical collusive agreements, involving downstream and upstream firms, using a setup of successive Cournot oligopolies. We show that a stable vertical agreement always exists: the unanimous vertical agreement involving all downstream and upstream firms. Thus, stable vertical collusive agreements exist even for market structures in which horizontal cartels would be unstable. We also show that there are economies for which the unanimous agreement is not the only stable one.
    Keywords: collusion, stability, vertical agreement.
    JEL: D43 L13
    Date: 2013
  9. By: Ahmad Naimzada; Marina Pireddu
    Abstract: We develop a model with intra-generational consumption externalities, based on the overlapping generation version of Diamond (1965) model. More specifically, we consider a two-period lived overlapping generation economy, assuming that the utility of each consumer depends also on the average level of consumption by other consumers in the same generation. In this way we obtain a positional game embedded in an overlapping generation economy. We characterize the consumption and saving choices for the two periods in the Nash equilibrium path and we determine a dynamic equation for capital accumulation coherent with the agents' choices in the Nash equilibrium. Hence, also the behavior, both static and dynamic, described by the equation for the capital accumulation is coherent with the Nash equilibrium. For the associated dynamical system we find a unique positive steady state for capital, which is globally stable. Its position is decreasing with respect to positive variations in the degree of interaction in the first period, while the opposite relation holds in the second period. We then compare the steady states for capital with and without social interaction. In this respect we show that the steady state with social interaction is larger than the steady state in the absence of social interaction if and only if the degree of interaction in the second period exceeds the degree of interaction in the first period. In particular, if the degrees of interaction in the two periods coincide, the dynamical system is equivalent to the one without social interaction.
    Keywords: Positional game, overlapping generations, consumption externalities
    JEL: C72 D91 E21 O41
    Date: 2013–06
  10. By: Jan Christoph Schlegel
    Abstract: In this note, I extend the work of Echenique (Amer. Econ. Rev. 102(1): 594-601, 2012) to show that under the assumption of unilaterally substitutable preferences a matching market with contracts may be embedded into a matching market with salaries. In particular, my result applies to the recently studied problem of cadet-to-branch matching.
    Keywords: Matching; Matching with contracts; Matching with salaries; Embedding; Substitutes; Unilateral substitutes
    JEL: C78
    Date: 2013–06
  11. By: Walter Bossert; Hans Peters
    Abstract: Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of singlebasinedness in a choice-theoretic setting. In conjunction with independence of irrelevant alternatives, single-basined choice implies a structure that conforms to the motivation underlying our definition. We also establish the consequences of requiring single-basined choice correspondences to be upper semicontinuous, and of the revealed preference relation to be Suzumura consistent.
    Keywords: Single-basinedness, choice correspondences, independence of irrelevant alternatives, upper semicontinuity, Suzumura consistency
    JEL: D11 D71
    Date: 2013
  12. By: Björn Vollan; Sebastian Prediger; Markus Frölich
    Abstract: We examine the effectiveness of three democratically chosen rules that alleviate the coordination and cooperation problems inherent in collectively managed common-pool resources. In particular we investigate how rule effectiveness and rule compliance depends on the prevailing local norms and ecological values held by resource users. For this purpose, we employ a framed field experiment that is based on a rangeland model for semi-arid regions and carried out with communal farmers in Namibia and South Africa. Participants could vote for three ‘best practice’ management rules found in many places around the world that are discussed for implementation in the study area: (temporary) private property rights, rotational grazing or limitation of livestock numbers. All rules were designed in a way that facilitated cooperation or coordination of actions. The focus of this study lies on the interactions between these rules and prevalent ecological norms exhibited in the rounds prior to rule implementation. In contrast to previous lab experimental studies, we find that democratic voting of rules is not sufficient for high rule compliance and an overall enhancement in cooperation. Rules turned out to be inefficient if they were in conflict with the prevalent ecological norm.
    Keywords: field laboratory experiment, rule compliance, ecological norms, common-pool resource, adaptive co-management, Southern Africa
    JEL: C71 C92 Q24
    Date: 2013–06

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