Search results for "GAME"
showing 10 items of 1663 documents
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…
Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity
2018
Abstract This paper focuses on multiproduct trading with indivisibilities and where a representative agent may have non-monotonic preferences. In this framework, the set of firms’ profits (which comes from efficient subgame perfect Nash equilibria) is the Pareto frontier of some projection of the core of the game. We show that under monotonicity efficient subgame perfect Nash equilibria are achieved by single offers and the equilibrium characterization is easy to obtain. When dealing with non-monotonic preferences the problem becomes more challenging. Then, we define a pair of primal–dual linear programming problems that fully identifies the core of the game. A set of modified versions of t…
A mixed 0-1 linear programming approach to the computation of all pure-strategy nash equilibria of a finite n -person game in normal form
2014
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2014/640960 A main concern in applications of game theory is how to effectively select a Nash equilibrium, especially a pure-strategy Nash equilibrium for a finite n -person game in normal form. This selection process often requires the computation of all Nash equilibria. It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is difficult to solve by naive enumeration algorithms. By exploiting the properties of pure strategy and multilinear terms in the payoff functions, this p…
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 …
Consensus in inventory games
2008
This paper studies design, convergence, stability and optimality of a distributed consensus protocol for n-player repeated non cooperative games under incomplete information. Information available to each player concerning the other players' strategies evolves in time. At each stage (time period), the players select myopically their best binary strategy on the basis of a payoff, defined on a single stage, 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 reordering or not from a common warehouse. As information evolves in time, the number of active players changes t…
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.
Negative results in the theory of games with lexicographic utilities
2003
When players may have lexicographic utilities, there are: (i) extensive games having a non-empty set of equilibria but empty sets of sequentially rational, sequential and perfect equilibria (ii) normal form games having a non-empty set of equilibria but an empty set of proper equilibria and no stable set of equilibria and (iii) two extensive games having the same normal form representation and disjoint sets of sequential equilibria.
Proportional Small Sample Bias in Pricing Kernel Estimations
2014
Numerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In a first step, we analyze theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader of potential computational issues coupled with statistical techniques. In a second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that estimated pricing kern…
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…