Search results for "Epsilon-equilibrium"
showing 8 items of 8 documents
On the Coincidence of the Feedback Nash and Stackelberg Equilibria in Economic Applications of Differential Games
2002
In this paper the scope of the applicability of the Stackelberg equilibrium concept in differential games is investigated. Firstly, conditions for obtaining the coincidence between the Stackelberg and Nash equilibria are defined in terms of the instantaneous pay-off function and the state equation of the game. Secondly, it is showed that for a class of differential games with state-interdependence both equilibria are identical independently of the player being the leader of the game. A survey of different economic models shows that this coincidence is going to occur for a good number of economic applications of differential games. This result appears because of the continuous-time setting i…
Multiproduct trading with a common agent under complete information: Existence and characterization of Nash equilibrium
2014
This paper focuses on oligopolistic markets in which indivisible goods are sold by multiproduct firms to a continuum of homogeneous buyers, with measure normalized to one, who have preferences over bundles of products. Our analysis contributes to the literature on private, delegated agency games with complete information, extending the insights by Chiesa and Denicolò (2009) to multiproduct markets with indivisibilities and where the agent's preferences need not be monotone. By analyzing a kind of extended contract schedules -mixed bundling prices- that discriminate on exclusivity, the paper shows that efficient equilibria always exist in such settings. There may also exist inefficient equil…
Consensus in Noncooperative Dynamic Games: a Multi-Retailer Inventory Application
2008
We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto op…
Distributed Consensus in Noncooperative Inventory Games
2009
This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a …
Existence and Optimality of Nash Equilibria in Inventory Games
2005
Abstract This paper studies the stability and optimality of a distributed consensus protocol for n -player repeated non cooperative games under incomplete information. At each stage, the players choose binary strategies and incur in a payoff monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in whether reordering or not from a common warehouse. The authors focus on Pareto optimality as a measure of coordination of reordering strategies, proving that there exists a unique Pareto optimal Nash equilibrium that verifies certain stability conditions.
Heterogeneous network games: Conflicting preferences
2013
Proceeding at: 2nd Annual UECE Lisbon Meeting: Game Theory and Applications, took place 2010, November, 4-6, in Lisbon (Portugal). The event Web site http://pascal.iseg.utl.pt/~uece/lisbonmeetings2010/ In many economic situations, a player pursues coordination or anti-coordination with her neighbors on a network, but she also has intrinsic preferences among the available options. We here introduce a model which allows to analyze this issue by means of a simple framework in which players endowed with an idiosyncratic identity interact on a social network through strategic complements or substitutes. We classify the possible types of Nash equilibria under complete information, finding two thr…
Noncooperative dynamic games for inventory applications: A consensus approach
2008
We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…
Introspection and equilibrium selection in 2 � 2 matrix games
1994
Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite siniple games, as 2x2 games with two strict Nash equilibria. Our paper models the introspection process by which the selected equilibrium is achieved in this class of games. Players begin their analysis with imprecise priors, obtained under weak restrictions formulated as Axioms. For a large class of reasoning dynamics we obtain as the solution the risk dominant Nash equilibrium.