2,155 research outputs found
Communication and equilibrium in discontinuous games of incomplete information
This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence
Equilibria Existence in Regular Discontinuous Games
Many conditions have been introduced to weaken the continuity re- quirements for equilibrium existence in games. We introduce a new con- dition, called regularity, that is simple and easy to verify. It is implied both by Reny's better-reply security and Simon and Zame's endogenous sharing rule method. Regularity implies that the limits of epsilon-equilibria are equilibria. Since this condition is weak, it is yet not enough to ensure pure strategy equilibrium existence, but we are able to identify extra conditions that, together with regularity, are sufficient for equilibrium existence. One is the marginal continuity property introduced by Prokopovych (2008), while the second is the well behavior of a sequence of approximating con- tinuous functions. In this way, we provide new equilibrium existence re- sults for discontinuous games under conditions that are simpler and easier to check than most of the available alternatives.
Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies
We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixed-strategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games
Competition between market-making Intermediaries
We introduce capacity constrained competition between market-making intermediaries in a model in which agents can choose between trading with intermediaries, joining a search market or remaining inactive. Recently, market-making by a monopolistic intermediary has been analyzed by Rust and Hall (2003) and Gehrig (1993). Market-makers set publicly observable ask and bid prices. Because market-making involves price setting, without further restrictions competition between market-making intermediaries is Bertrand-like and yields the Walrasian outcome, where the ask-bid spread is zero (Rust and Hall 2003, Gehrig 1993). However, positive ask-bid spreads and competition between market-makers can be observed in reality, e.g. in banking and in retailing. Following Kreps and Scheinkman (1983) and Boccard and Wauthy (2000), we therefore introduce physical capacity constraints. This allows for a gradual transition from monopolistic to perfectly competitive intermediation as the number of intermediaries increases. In particular, we show that given Cournot capacities, intermediaries will set Cournot bid and ask prices in the subsequent subgames, so that the equilibrium of the intermediated market coincides with the Walrasian equilibrium as the number of intermediaries becomes largeMarket-making, capacity constrained competition, market microstructure
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Convexity on Nash Equilibria without Linear Structure
To give sucient conditions for Nash Equilibrium existence in a continuous game is a central problem in Game Theory. In this paper, we present two games in which we show how the continuity and quasi-concavity hypotheses are unconnected one to each other. Then, we relax the quasiconcavity assumption by exploiting the multiconnected convexity's concept (Mechaiekh & Others, 1998) in spaces without any linear structure. These results will be applied to two non-zero-sum games lacking the classical assumptions and more recent improvements (Ziad, 1997), (Abalo & Kostreva, 2004). As a minor result, some counterexamples about relationship between some continuity conditions due to Lignola (1997), Reny (1999) and Simon (1995) for Nash equilibria existence are obtained.Nash Equilibria Existence; Fixed Point Theorem; Generalized Convexity; 2 Person Game; 3 Person Game; Symmetric Game; Generalized Continuity.
Riemannian game dynamics
We study a class of evolutionary game dynamics defined by balancing a gain
determined by the game's payoffs against a cost of motion that captures the
difficulty with which the population moves between states. Costs of motion are
represented by a Riemannian metric, i.e., a state-dependent inner product on
the set of population states. The replicator dynamics and the (Euclidean)
projection dynamics are the archetypal examples of the class we study. Like
these representative dynamics, all Riemannian game dynamics satisfy certain
basic desiderata, including positive correlation and global convergence in
potential games. Moreover, when the underlying Riemannian metric satisfies a
Hessian integrability condition, the resulting dynamics preserve many further
properties of the replicator and projection dynamics. We examine the close
connections between Hessian game dynamics and reinforcement learning in normal
form games, extending and elucidating a well-known link between the replicator
dynamics and exponential reinforcement learning.Comment: 47 pages, 12 figures; added figures and further simplified the
derivation of the dynamic
CHARACTERIZATION OF THE SUPPORT OF THE MIXED STRATEGY PRICE EQUILIBRIA IN OLIGOPOLIES WITH HETEROGENEOUS CONSUMERS
This paper revisits the theory of oligopoly pricing and shows that for a large class of demand and cost functions, a mixed strategy equilibrium necessarily implies that each firm’s equilibrium strategy is a discrete distribution over a finite number of prices.
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