nep-gth New Economics Papers
on Game Theory
Issue of 2011‒06‒11
twelve papers chosen by
Laszlo A. Koczy
Hungarian Academy of Sciences and Obuda University

  1. Leadership games with convex strategy sets. By von Stengel, Bernhard; Zamir, Shmuel
  2. Core-stable rings in auctions with independent private values. By Biran, Omer; Forges, Françoise
  3. Characterizing Compromise Stability of Games Using Larginal Vectors By Platz, T.T.; Hamers, H.J.M.; Quant, M.
  4. Follower payoffs in symmetric duopoly games. By von Stengel, Bernhard
  5. On uniqueness and stability of symmetric equilibria in differentiable symmetric games By Andreas Hefti
  6. Learning From a Piece of Pie By Pierre-Andre Chiappori; Olivier Donni; Ivana Komunje
  7. A Measure to compare Matchings in Marriage Markets By Florian M. Biermann
  8. Game Theoretic Analysis of Negotiations under Bankruptcy By Amira Annabi; Michèle Breton; Pascal François
  9. A dynamic school choice model By Juan Sebastián Pereyra
  10. House allocation with overlapping generations By Kurino Morimitsu
  11. The Emergence of Leadership in Social Networks By T. Clemson; T. S. Evans
  12. Satiated economies with unbounded consumption sets : fuzzy core and equilibrium. By Nizar Allouch; Monique Florenzano

  1. By: von Stengel, Bernhard; Zamir, Shmuel
    Abstract: A basic model of commitment is to convert a two-player game in strategic form to a “leadership game” with the same payoffs, where one player, the leader, commits to a strategy, to which the second player always chooses a best reply. This paper studies such leadership games for games with convex strategy sets. We apply them to mixed extensions of finite games, which we analyze completely, including nongeneric games. The main result is that leadership is advantageous in the sense that, as a set, the leader's payoffs in equilibrium are at least as high as his Nash and correlated equilibrium payoffs in the simultaneous game. We also consider leadership games with three or more players, where most conclusions no longer hold.
    Date: 2010–07
  2. By: Biran, Omer; Forges, Françoise
    Abstract: We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders' final utility possibly depends on the winner's identity. We show that such direct externalities offer a possible explanation for cartels'structures (not) observed in practice.
    Keywords: Core; Bayesian game; Auctions; Collusion; partition function game;
    JEL: D44 C72 C71
    Date: 2011
  3. By: Platz, T.T.; Hamers, H.J.M.; Quant, M. (Tilburg University, Center for Economic Research)
    Abstract: The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an order of the players and describes the efficient payoff vector giving the first players in the order their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. In this paper we describe two ways of characterizing sets of larginal vectors that satisfy the condition that if every larginal vector of the set is a core element, then the game is compromise stable. The first characterization of these sets is based on a neighbor argument on orders of the players. The second one uses combinatorial and matching arguments and leads to a complete characterization of these sets. We find characterizing sets of minimum cardinality, a closed formula for the minimum number of orders in these sets, and a partition of the set of all orders in which each element of the partition is a minimum characterizing set.
    Keywords: Core;core cover;larginal vectors;matchings.
    JEL: C71
    Date: 2011
  4. By: von Stengel, Bernhard
    Abstract: This paper compares the leader and follower payoff in a duopoly game, as they arise in sequential play, with the Nash payoff in simultaneous play. If the game is symmetric, has a unique symmetric Nash equilibrium, and players' payoffs are monotonic in the opponent's choice along their own best reply function, then the follower payoff is either higher than the leader payoff, or even lower than in the simultaneous game. This gap for the possible follower payoff had not been observed in earlier duopoly models of endogenous timing.
    Date: 2010–07
  5. By: Andreas Hefti
    Abstract: Higher-dimensional symmetric games become of more and more importance for applied micro- and macroeconomic research. Standard approaches to uniqueness of equilibria have the drawback that they are restrictive or not easy to evaluate analytically. In this paper I provide some general but comparably simple tools to verify whether a symmetric game has a unique symmetric equilibrium or not. I distinguish between the possibility of multiple symmetric equilibria and asymmetric equilibria which may be economically interesting and is useful to gain further insights into the causes of asymmetric equilibria in symmetric games with higher-dimensional strategy spaces. Moreover, symmetric games may be used to derive some properties of the equilibrium set of certain asymmetric versions of the symmetric game. I further use my approach to discuss the relationship between stability and (in)existence of multiple symmetric equilibria. While there is an equivalence between stability, inexistence of multiple symmetric equilibria and the unimportance of strategic effects for the comparative statics, this relationship breaks down in higher dimensions. Stability under symmetric adjustments is a minimum requirement of a symmetric equilibrium for reasonable comparative statics of symmetric changes. Finally, I present an alternative condition for a symmetric equilibrium to be a local contraction which is more general than the conventional approach of diagonal dominance and yet simpler to evaluate than the eigenvalue condition of continuous adjustment processes.
    Keywords: Symmetric games, Nash equilibrium, uniqueness, stability
    JEL: C72
    Date: 2011–05
  6. By: Pierre-Andre Chiappori (Columbia University - Department of Economics); Olivier Donni (Universitie de Cergy-Pontoise - Department of Economics); Ivana Komunje (University of California San Diego - Department of Economics)
    Abstract: We investigate the empirical content of the Nash solution to two-player bar-gaining games. The bargaining environment is described by a set of variables that may affect agents' preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither are the agents' utilities nor their threat points. We consider both a deterministic version of the model in which the econometrician observes the shares as deterministic functions of the variables under consideration, and a stochastic one in which because of latent disturbances only the joint distribution of incomes and outcomes is recorded. We show that in the most general framework any outcome can be rationalized as a Nash solution. However, even mild exclusion restrictions generate strong implications that can be used to test the Nash bargaining assumption. Stronger conditions further allow to recover the underlying structure of the bargaining, and in particular, the cardinal representation of individual preferences in the absence of uncertainty. An implication of this finding is that empirical works entailing Nash bargaining could (and should) use much more general and robust versions than they usually do.
    Date: 2011
  7. By: Florian M. Biermann
    Abstract: In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly "disruptive" subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: The subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.
    Keywords: Stable marriage problem, Matching, Blocking pair, Instability, Matching comparison, Decentralized market, Bargaining set
    Date: 2011–06
  8. By: Amira Annabi; Michèle Breton; Pascal François
    Abstract: We extend the contingent claims framework for the levered firm in explicitly modeling the resolution of financial distress under formal bankruptcy as a non-cooperative game between claimants under the supervision of the bankruptcy judge. The identity of the class of claimants proposing the first reorganization plan is found to be a key determinant of the likelihood of liquidation and of the renegotiated value of claims. Our quantitative results confirm the economic intuition that a bankruptcy design must trade-off the initial priority of claims with the viability of reorganized firms.
    Keywords: Bankruptcy procedure, game theory, dynamic programming
    JEL: C61 C7 G33 G34
    Date: 2011
  9. By: Juan Sebastián Pereyra (El Colegio de México)
    Abstract: This paper considers a real-life assignment problem faced by the Mexican Ministry of Public Education. Inspired by this situation, we introduce a dynamic school choice problem that consists in assigning positions to overlapping generations of teachers. From one period to another, agents are allowed either to retain their current position or to choose a preferred one. In this framework, a solution concept that conciliates the fairness criteria with the individual rationality condition is introduced. It is then proved that a fair matching always exists and that it can be reached by a modified version of the deferred acceptance algorithm of Gale and Shapley. We also show that the mechanism is dynamic strategy-proof, and respects improvements whenever the set of orders is lexicographic by tenure.
    Keywords: school choice, overlapping agents, dynamic matching, deferred acceptance algorithm
    JEL: C71 C78 D71 D78 I28
    Date: 2011–05
  10. By: Kurino Morimitsu (METEOR)
    Abstract: Many real-life applications of house allocation problems are dynamic. For example, each year college freshmen move in and seniors move out of on-campus housing. Each student stays on campus for only a few years. A student is a `newcomer’ in the beginning and then becomes an ''existing tenant.’ Motivated by this observation, we introduce a model of house allocation with overlapping generations. In terms of a dynamic rule without monetary transfers, we examine two static rules of serial dictatorship (SD) and top trading cycles (TTC), both of which are based on an ordering of agents and give a higher-order agent a more advantageous position in the assignment procedure. We support a seniority-based SD rule by showing its dynamic Pareto efficiency. Similarly, we support a seniority-based TTC rule under time-invariant preferences by showing its dynamic Pareto efficiency and incentive compatibility.
    Keywords: microeconomics ;
    Date: 2011
  11. By: T. Clemson; T. S. Evans
    Abstract: We study a networked version of the minority game in which agents can choose to follow the choices made by a neighbouring agent in a social network. We show that for a wide variety of networks a leadership structure always emerges, with most agents following the choice made by a few agents. We find a suitable parameterisation which highlights the universal aspects of the behaviour and which also indicates where results depend on the type of social network.
    Date: 2011–06
  12. By: Nizar Allouch (School of economics and Finance - Queen Mary University of London); Monique Florenzano (Centre d'Economie de la Sorbonne - Paris School of Economics)
    Abstract: For an exchange economy, under assumptions which did not bring about the existence of quasiequilibrium with dividends as yet, we prove the nonemptiness of the fuzzy rejective core. Then, via Konovalov (1998, 2005)'s equivalence result, we solve the equilibrium (with dividends) existence problem. In a last section, we show the existence of a Walrasian quasiequilibrium under a weak non-satiation condition which differs from the weak non-satiation assumption introduced by Allouch-Le Van (2009). This result, designed for exchange economies whose consumers' utility functions are not assumed to be upper semicontinuous, complements the one obtained by Martins-da-Rocha and Monteiro (2009).
    Keywords: Exchange economy, satiation, equilibrium with dividends, rejective core, fuzzy rejective core, core equivalence.
    JEL: D50
    Date: 2011–05

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