The dual reduction process, introduced by Myerson, allows to reduce a finite game into a smaller dimensional game such that any equilibrium of the reduced game is an equilibrium of the original game. This holds both for Nash equilibrium and correlated equilibrium. We present examples of applications of dual reduction and argue that this is a useful tool to study Nash equilibria and correlated e...

A road pricing game is a game where various stakeholders and/or regions with different (and usually conflicting) objectives compete for toll setting in a given transportation network to satisfy their individual objectives. We investigate some classical game theoretical solution concepts for the road pricing game. We establish results for the road pricing game so that stakeholders and/or regions...

This note studies the following question: If a researcher is given a finitely supported mixed strategy for each player over a continuous strategy space, does there exist a game whose unique Nash equilibrium is given by these mixed strategies? This note finds that any set of finitely supported mixed strategies on metric spaces can be represented as the unique Nash equilibrium to a separable game...

We consider a market game with a continuum of consumers, where the measure of each type is stochastic. Nature selects the set of active consumers, who make bids and o¤ers on ` ¡ 1 spot market trading posts. Existence of type-symmetric Nash equilibrium is proven. When facing price uncertainty, best responses are unique, and a Nash equilibrium to the sell-all game is typically not a Nash equilibr...

A non-cooperative game theoretical approach for analyzing opportunistic spectrum access in cognitive radio environments is proposed. New concepts from computational game theory are applied to spectrum access analysis in order to extract rules of behaviour for an emerging environment. In order to assess opportunistic spectrum access scenarios of cognitive radios, two oligopoly game models are re...

In this paper, we deal with a planar location-price game where firms first select their locations and then set delivered prices in order to maximize their profits. If firms set the equilibrium prices in the second stage, the game is reduced to a location game for which pure strategy Nash equilibria are studied assuming that the marginal delivered cost is proportional to the distance between the...

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model for such a capacity competition problem over a network. These two models are base...

This is an extended write-up of a lecture introducing the concept of Nash equilibrium in the context of an auction-type game that one can observe being played by “ordinary people” in real time. In a simplified model, we give an explicit formula for the Nash equilibrium. The actual game is more complicated and more interesting; players place a bid on one item (among several) during a time window...

We consider a two-player partial-information game on a Markov chain, where each player attempts to minimize its own cost over a finite time horizon. We show that this game has always a Nash equilibrium in stochastic behavioral policies. The technique used to prove this result is constructive but has severe limitations because it involves solving an extremely large bi-matrix game. To alleviate t...