Sharing of spectrum has been identified as a key requirement in cognitive radio networks(CRNs). We address the problem of spectrum sharing with spectrum pricing where the primary user wants to sell the spectrum to the secondary users. By equilibrium pricing scheme, each of the players in the spectrum sharing game aims to take the strategy which maximize its own profit under sojourn-time constra...

Bertrand competition under decreasing returns involves a wide interval of pure strategy equilibrium prices. We first present results of experiments in which two, three and four identical firms repeatedly interact in this environment. Less collusion with more firms leads to lower average prices. With more than two firms, the predominant market price is 24, a price not predicted by conventional e...

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition y...

This paper develops a theoretical foundation for the undercut-proof equilibrium (see Shy, 1996, 2002; Morgan and Shy, 2013). In a general spatial setting, the set of undercut-proof prices is equivalent the core of a non-transferable utility cooperative-game, played on the set of outcomes that are feasible in Bertrand competition. The result depends critically on two conditions: First, firms mus...

We show the existence of Nash equilibria in a Bertrand oligopoly price competition game using a possibly asymmetric attraction demand model with convex costs under mild assumptions. We show that the equilibrium is unique and globally stable. To our knowledge, this is the first paper to show the existence of a unique equilibrium with both non-linear demand and non-linear costs. In addition, we g...

Static and dynamic games are important tools for the analysis of strategic interactions among economic agents and have found many applications in economics. In many games equilibria can be described as solutions of polynomial equations. In this paper we describe state-of-the-art techniques for finding all solutions of polynomial systems of equations and illustrate these techniques by computing ...

Bertrand competition under decreasing returns involves a wide interval of pure strategy equilibrium prices. We first present results of experiments in which two, three and four identical firms repeatedly interact in this environment. Less collusion with more firms leads to lower average prices. With more than two firms, the predominant market price is 24, a price not predicted by conventional e...

We study oligopoly price competition between multiproduct firms, firms whose products interact in the profit function. Specifically, we focus on the impact of intra-firm product interactions on the level of equilibrium profits. This impact is divided into two effects: a direct effect and a strategic effect (i.e., through the competitors’ actions). We derive conditions such that the strategic ef...

In a class of games including some Cournot and Bertrand games, a sequence of plays converges to the unique Nash equilibrium if and only if the sequence is “consistent with adaptive learning” according to the new definition we propose. In the Arrow-Debreu model with gross substitutes, a sequence of prices converges to the competitive equilibrium if and only if the sequence is consistent with ada...

We look at the impact of a binding minimum wage on labor market outcomes and welfare distributions in a partial equilibrium model of matching and bargaining in the presence of on-the-job search. We use two different specifications of the Nash bargaining problem. In one, firms engage in a Bertrand competition for the services of an individual, as in Postel-Vinay and Robin (2002). In the other, f...