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The power of a recent result for Nash equilibria of sum-aggregative games is illustrated by providing a variant of Ewerhart's equilibrium uniqueness theorem for Cournot oligopolies with a biconcave essential price function. This variant, contrary to the original result, allows for industry revenue that is discontinuous at 0 and can be considered a major generalization of the classical uniqueness result of Szidarovszky and Okuguchi for rent-seeking games. It assumes that the elasticity of the price function has a limit when its argument tends to zero.
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Recently a framework was developed for aggregative variational inequalities by means of the Selten-Szidarovszky technique. By referring to this framework, a powerful Nash equilibrium uniqueness theorem for sum-aggregative games is derived. Payoff functions are strictly quasi-concave in own strategies but may be discontinuous at the origin. Its power is illustrated by reproducing and generalising in a few lines an equilibrium uniqueness result in Corchon and Torregrosa (2020) for Cournot oligopolies with the Bulow-Pfleiderer price function. Another illustration addresses an asymmetric contest with endogenous valuations in Hirai and Szidarovszky (2013).
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We present a game theoretic model of media bias based on the Pure Location Hotelling Game. Contrary to the usual restrictive assumption of inelastic demand, we allow that demand is elastic and introduce in this context the concepts of quite inelastic and quite elastic demand. The real world interpretation of the media bias model is explained in detail for its discrete variant for unlimited media providers and arbitrary distribution of individuals.
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We enrich the theory of variational inequalities in the case of an aggregative structure by implementing recent results obtained by using the Selten-Szidarovszky technique. We derive existence, semi-uniqueness and uniqueness results for solutions and provide a computational method. As an application we derive very powerful practical equilibrium results for Nash equilibria of sum-aggregative games and illustrate with Cournot oligopolies.
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Various Nash equilibrium results for a broad class of aggregative games are presented. The main ones concern equilibrium uniqueness. The setting presupposes that each player has ℝ+ as strategy set, makes smoothness assumptions but allows for a discontinuity of stand-alone payoff functions at 0; this possibility is especially important for various contest and oligopolistic games. Conditions are completely in terms of marginal reductions which may be considered as primitives of the game. For many games in the literature they can easily be checked. They automatically imply that conditional payoff functions are strictly quasi-concave. The results are proved by means of the Szidarovszky variant of the Selten-Szidarovszky technique. Their power is illustrated by reproducing quickly and improving upon various results for economic games.
We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f(d) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-reply potential. This result holds in particular for f(d) = wd with 0 < w ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made.
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The Hotelling pure location game is revisited. It is assumed that there there are two identical players, strategy sets are one-dimensional and demand as a function of distance is constant or strictly decreasing. Besides qualitative properties of conditional payoff functions, attention is given to the structure of the equilibrium set, best-response correspondences and existence of potentials.
The paper examines the claim that a virtuous cycle of more secure land rights, more land-saving investments, and denser populations requires the development of institutions that regulate competition over land. We construct a contest model that links the tenure security-investment relationship to the efforts of land users to enhance land rights themselves and the role of institutional protection. We study the impact of population growth on a close-to-subsistence economy, including the possibility that it weakens institutional protection. We derive sufficient conditions for a positive effect on land investment, but also show that population growth can push the economy into a low-productivity trap.
Coalition formation is often analysed in an almost non-cooperative way as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalise this widely used approach for the case where in each stage actions are simultaneous. There is special attention to the case of a symmetric physical game. Various theoretical results, in particular for cartel games, are provided. As they are crucial, also recent results on uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives.
We consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and a proper price function p̃ with decreasing price flexibility. This class allows for (at 0) discontinuous industry revenue and in particular for p̃(y) = y- α. The paper illustrates in an exemplary way the Selten-Szidarovszky technique based on virtual backward reply cspondences. An algorithm for the calculation of the unique equilibrium is provided.
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For binary action games we present three properties which have in common that they are defined by conditions on marginal payoffs. The first two properties guarantee the existence of a special type of Nash equilibrium called semi-strict Nash equilibrium, for which we also show an algorithm to locate. The third one guarantees the existence of an exact potential, and can realize the aforementioned two properties in a class of exact potential games. The first one guarantees the existence of a generalized ordinal potential. Each symmetric binary action game possesses all the three properties. The results are illustrated by three applications.
We study a rather simplified game model of competition for status. Each player chooses a scalar variable (say, the level of conspicuous consumption), and then those who chose the highest level obtain the "high" status, while everybody else remains with the "low" status. Each player strictly prefers the high status, but they also have intrinsic preferences over their choices. The set of all feasible choices may be continuous or discrete, whereas the strategy sets of different players can only differ in their upper and lower bounds. The resulting strategic game with discontinuous utilities does not satisfy the assumptions of any general theorem known as of today. Nonetheless, the existence of a (pure strategy) Nash equilibrium, as well as the "finite best response improvement property", are established.
