International Game Theory Review

This paper deals with duopoly models with vertical product differentiation. These are two-stage games. In the first stage, the quality game, the two firms choose their quality. In the second stage, the price game, they choose their prices. When the market is covered, the properties of this game are well known, even when the consumers are not uniformly distributed. When the market is uncovered the literature is not always clear about these models. In the present paper it is shown that the price game can be solved, when the consumers are distributed according to a distribution function with a log-concave density function.

The weighted value was introduced by Shapley in 1953 as an asymmetric version of his value. Since then several axiomatizations have been proposed including one by Shapley in 1981 specifically addressed to cost allocation, a context in which weights appear naturally. It was at the occasion of a comment in which he only stated the axioms. The present paper offers a proof of Shapley's statement as well as an alternative set of axioms. It is shown that the value is the unique rule that allocates additional fixed costs fairly: only the players who are concerned contribute to the fixed cost and they contribute in proportion to their weights. A particular attention is given to the case where some players are assigned a zero weight.

In this paper, we present a matching market in which an institution has to hire a set of pairs of complementary workers, and has a quota that is the maximum number of candidates pair positions to be filled. We define a stable solution and first show that in the unrestricted institution preferences domain, the set of stable solution may be empty and second we obtain a complete characterization of the stable sets under responsive restriction of the institution's preference.

This paper combines the imperfect reliability model of Bala and Goyal [2000b] with the heterogeneous player model of Galeotti et al. [2006]. We compare existence, characterization and efficiency results in the resulting framework with the results in other frameworks allowing for imperfect reliability or heterogeneity. Specifically, we compare our work with the framework of Haller and Sarangi [2005] which allows for heterogeneity in link reliability but assumes that players are homogeneous. We find, by contrast with their paper, that non existence of Nash networks is possible in our framework even if the population is very small. Moreover, although the incentives of players to maintain (or delete) links are different, in both frameworks there exist parameters such that every essential network is strict Nash and efficient.

We conceive of a player in dynamic games as a set of agents, which are assigned the distinct tasks of reasoning and node-specific choices. The notion of agent connectedness measuring the sequential stability of a player over time is then modeled in an extended type-based epistemic framework. Moreover, we provide an epistemic foundation for backward induction in terms of agent connectedness. Besides, it is argued that the epistemic independence assumption underlying backward induction is stronger than usually presumed.

We examine a vertically differentiated duopoly where firms invest in process and product innovation and then compete in prices under full market coverage. We show that (i) process innovation fosters (hinders) product innovation for the low-quality (high-quality) firm; (ii) the firm which is initially more efficient invests more than the rival in process innovation; (iii) if the initial differential between marginal costs is sufficiently high, the demand for the less efficient firm is nil and the duopoly equilibrium does not exist.

In this paper we study and compute E-points in an explicit way for a special general kind of 3k + 1 and 3k + 2 players.

The interaction between a sophisticated player and a fictitious player is analyzed and applied to the problem of optimal enforcement. An adaptive potential offender myopically responds to the history of past enforcement. How can a sophisticated enforcement official take advantage of this behavior? Will compliance with the law be attained? Conditions under which full compliance arises is derived and the optimal cycle of enforcing and not enforcing the law is presented. Welfare is shown to be greater than if the offender was sophisticated as well.