International Game Theory Review

We propose a model of retail promotions for competitive distribution channels and investigate whether cooperative advertising programs are profitable for such channels. While previous studies showed that coop programs increase total channel profits in bilateral monopolies, no evidence of such a result has been provided for channels where competition is present at the manufacturing and the retailing levels. In this paper, we consider a distribution channel formed by two manufacturers and two retailers and propose a model that accounts for brand and store substitution effects generated by the retailer's promotional efforts. The efficiency of the coop plan is investigated by comparing equilibria of four non-cooperative games; one where manufacturers do not offer any promotional support to the retailers, one where manufacturers do offer such a support and two scenarios where in turn only one manufacturer is offering such program. We show that when competition is introduced, coop ad programs may be due to a prisonner's dilemma situation for the manufacturers. The benefit for retailers and consumers is also assessed.

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.

The literature on advertising and promotions can be divided in two categories. A first group of models assume that promotion contributes (positively) to the goodwill towards the product, and a second group assumes that promotions reduce that goodwill. In this paper we build a differential game model where the impact of promotion on goodwill is endogenously determined. We conduct a comparative dynamics exercise. An unexpected result is that an increase in the sensitivity of sales to goodwill can lead to a decrease of the equilibrium level of sales.

The paper investigates under which additional assumptions the bargaining set, the reactive bargaining set or the semireactive bargaining set coincides with the core on the class of symmetric TU-games. Furthermore, we give an example which illustrates that the property 'the bargaining set coincides with the core' is not a prosperity property.

The general approach for the pricing of rainbow (or colored) options with fixed transaction costs is developed from the game theoretic point of view. The evolution of the underlying common stocks is considered in discrete time. The main result consists in the explicit calculation of the hedge price for a variety of the rainbow options including option delivering the best of J risky assets and cash, calls on the maximum of J risky assets and the multiple-strike options. The results obtained can be also used in the framework of real options.

We examine the long-run outcomes under free entry-exit when each firm not only takes account of the effects of her own entry-exit on the market structure but also takes full account of the effects due to other firms' simultaneous entry-exit. Adopting the framework of the theory of social situations (TOSS), we derive a unique set of stable outcomes, which is based only on two fundamental assumptions of the "firms-as-profit-maximizers" and the "free entry-exit," but not on any specific mode of play (i.e., a specification of how the players make their decisions, take actions within the market, and think of the other players' behavior). We compare the stable outcome with the long-run equilibria under the competitive mode, the Cournot-Nash mode, and the monopolistically competitive mode. We find that (i) each of these equilibria can be compatible with the stable outcome only if the market size is small and (ii) none of them can be compatible with the stable outcome if the market size is sufficiently large; Further, (iii), for almost all market size, the monopolistically competitive equilibrium is compatible with the stable outcome if the elasticity of substitution is sufficiently close to (but, greater than) unity. In a sense, when the market size is sufficiently large, these three modes of play are not consistent with two fundamental assumptions.

In this paper, we try to analyze the interactions among the shippers and the carriers, including the rail and marine shipping industry, in the bulk shipping market. Our paper presents both a two-player game model, and a two-stage, three-player, game model that includes the buyer as an active player. Assuming the players have complete information, we derive an analytical solution to a two-stage, three-player game with capacity constraints. We also present a numerical algorithm to solve a two-stage, three-player game with complete information. A grain transportation scenario in the Great Lakes and St. Lawrence Seaway is used to illustrate our models. The results suggest that the two-stage, three-player game model has a better prediction capability than the duopoly game model in the bulk shipping competition problem.

We define a duality of solutions in coalitional games that we call a twisted duality. This twisted duality extends the rule of self-duality in bankruptcy problems. After showing that the prekernel and prenucleolus exhibit twisted duality, we define a twisted reduced game property and characterize the prekernel and prenucleolus by axioms including this property. We note that the Shapley value satisfies twisted duality, and we define another twisted reduced game property by and characterize the Shapley value by axioms including this property.

The paper presents a coalition-structure value that is meant to capture outside options of players in a cooperative game. It deviates from the Aumann-Drèze value by violating the null-player axiom. We use this value as a power index and apply it to weighted majority games.

I study the robustness of Rubinstein's (1989) E-Mail Game results by varying the information that players can utilize. The article follows one of Morris' (2002) reactions to the E-Mail game "that one should try to come up with a model of boundedly rational behavior that delivers predictions that are insensitive to whether there is common knowledge or a large number of levels of knowledge". Players in my model are presumed to use 'rough inductive reasoning' because they cannot utilize exact information.

The information structure in the E-Mail game is generalized and the conditions are characterized under which Rubinstein's results hold. I find that rough inductive reasoning generates a payoff dominant equilibrium where the expected payoffs change continuously (instead of discretely) in the probability of "faulty" communication.

In this short note we extend the very well known Centipede game of Rosenthal to the same extensive games with perfect information. The only difference that here the Centipede games have instead of numbers as payoff functions, they have variables. We introduce and study the relationship between the structure of subgame perfect equilibrium points (see Osborne (1994), Binmore (1994)) and the friendly equilibrium points due to Marchi (2004a) and (2004b). We solve an Asheim's conjecture (private communication).

We develop an interactive model involving competitive tax evasion to determine optimal transfer prices by multinational firms. We establish that the proposed game is characterized by multiple equilibria. Implications of these multiple equilibria are examined.

Different axiomatizations of the Shapley value for TU games can be found in the literature. The Shapley value has been generalized in several ways to the class of games in partition function form. In this paper we discuss another generalization of the Shapley value and provide a characterization.

Consider the cooperative coalition games with side payments. Bargaining sets are calculated for all possible coalition structures to obtain a collection of imputations rather than single imputation. Our aim is to obtain a single payoff vector, which is acceptable by all players of the game under grand coalition. Though Shapely value is a single imputation, it is based on fair divisions rather than bargaining considerations. So, we present a method to obtain a single imputation based on bargaining considerations.

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation.

In this paper, we study the immunity of bankruptcy rules to manipulation via merging or splitting agents' claims. We focus on the TAL-family of bankruptcy rules (Moreno-Ternero & Villar, 2006), a one-parameter family encompassing three classical rules: the Talmud (T) rule, the constrained equal-awards (A) rule and the constrained equal-losses (L) rule. We show that all rules within the TAL-family are partially non-manipulable and identify the domain of problems where each rule is either non-manipulable by merging or non-manipulable by splitting. We also show that they can be ranked in terms of their relative non-manipulability, according to the parameter that generates the family.