Guilherme Carmona
University of Surrey
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Featured researches published by Guilherme Carmona.
Journal of Economic Theory | 2009
Guilherme Carmona
We introduce a notion of upper semicontinuity, weak upper semicontinuity, adn show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games.
Journal of Economic Theory | 2009
Guilherme Carmona; Konrad Podczeck
Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler [D. Schmeidler, Equilibrium points of nonatomic games, J. Stat. Phys. 4 (1973) 295-300], Rashid [S. Rashid, Equilibrium points of non-atomic games: Asymptotic results, Econ. Letters 12 (1983) 7-10], Mas-Colell [A. Mas-Colell, On a theorem by Schmeidler, J. Math. Econ. 13 (1984) 201-206], Khan and Sun [M. Khan, Y. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999) 455-492] and Podczeck [K. Podczeck, On purification of measure-valued maps, Econ. Theory 38 (2009) 399-418]. The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games. In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games.
Journal of Economic Theory | 2009
Mehmet Barlo; Guilherme Carmona; Hamid Sabourian
We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an [epsilon]-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.
Journal of Economic Theory | 2014
Guilherme Carmona; Konrad Podczeck
Balders (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky (2011) and Barelli and Meneghel (2012) for finite-players games, to games with a measure space of players and establish the existence of pure strategy Nash equilibrium for such games. A specification of our main existence result is provided which is ready to fit the needs of applications. As an illustration, we consider several optimal income tax problems in the spirit of Mirrlees (1971) and use our game-theoretic result to show the existence of an optimal income tax in each of these problems.
Games and Economic Behavior | 2009
Guilherme Carmona; José Fajardo
We establish the existence of subgame perfect equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a subgame perfect equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal choices for the agent. Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861-872] designed for discontinuous games.
World Scientific Books | 2013
Guilherme Carmona
The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship between them has not been explained clearly. The book will make these results easily accessible and understandable to researchers in the field. Contents: Introduction Continuous Normal-Form Games Generalized Better-Reply Secure Games Stronger Existence Results Limit Results Games With an Endogenous Sharing Rule Games With a Continuum of Players Readership: Graduate students, researchers and professionals interested in mathematical economics and game theory. Key Features: First book to describe recent developments in the existence and stability of Nash equilibrium Presents research results in existence and stability of Nash equilibrium in an easily accessible manner
Games and Economic Behavior | 2012
Guilherme Carmona; Konrad Podczeck
We present a result on approximate ex-post stability of Bayes–Nash equilibria in semi-anonymous Bayesian games with a large finite number of players. The result allows playersʼ action and type spaces to be general compact metric spaces, thus extending a result by Kalai (2004).
International Journal of Game Theory | 2006
Guilherme Carmona
We study the properties of finitely complex, symmetric, globally stable, and semi-perfect equilibria. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. Our second main result is a strong anti-Folk Theorem, since, in contrast to what is described by the Folk Theorem, the set of equilibrium payoffs does not expand when the game is repeated.
Journal of Economic Theory | 2016
Mehmet Barlo; Guilherme Carmona; Hamid Sabourian
We show that the Folk Theorem holds for n-player discounted repeated games with bounded-memory pure strategies. Our result requires each player’s payoff to be strictly above the pure minmax payoff but requires neither time-dependent strategies, nor public randomization, nor communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions.
Journal of Economic Theory | 2018
Guilherme Carmona; Konrad Podczeck
We consider games with an endogenous sharing rule and provide conditions for the invariance of the equilibrium set, i.e., for the existence of a common equilibrium set for the games defined by each possible sharing rule. Applications of our results include Bertrand competition with convex costs, electoral competition, and contests.