International Game Theory Review

This paper reports on an experiment designed to explore the robustness of the deadline effect in multi period bargaining games using constant and decreasing pies, different time horizons, and constant and alternating roles. Our results indicate that decreasing pies and alternating roles lead to earlier agreements (i.e., attenuate the deadline effect) although only alternating roles significantly reduce the number of conflicts.

We consider a manufacturer's dual distributions channels consisting on the one hand of a virtual (online) channel operated directly by a manufacturer and on the other hand of a real (offline) channel operated by an intermediate retailer. Customers are assumed heterogeneous in their virtual acceptance, deriving a surplus according to the channel they shop at. Assuming that customers' derived benefits are random with a known probability distribution, we obtain a probabilistic model, which is used to construct an inter-temporal model for shopping online. In addition, we suppose that the retailer uses a markup pricing strategy and has a strategic role. This results in a Stackleberg differential game where the manufacturer is leader and the retailer is a follower. The optimal policy shows that the manufacturer charges the same price across both channels. This finding is consistent with classical results in economics. However, our research goes beyond this observation and indicates that the online price, the retailer's markup and the probability to buy are affected by consumers' heterogeneity in a specific manner. Moreover, we show that while the retailer sets a price equal to the product value, the online price is lower and is equal to the product value less the guarantee provided by the manufacturer for the risk the customer take to buy online. This guarantee is not discriminating and is set to the risk of the customer with the lowest virtual acceptance. Finally, we show that the introduction of the online store is a win-win strategy; both the customers and the manufacturer are better off.

The impossibility of speculative trade result (Milgrom and Stokey, 1982) provokes the questions why traders care about their private information, if they cannot profit from it and how the aggregate information can then be reflected in REE prices. This paper answers these questions by analyzing a speculative market as a game, which has the advantage of making the equilibrium strategies explicit. We introduce the new equilibrium selection concept of best reply resistance, which singles out those equilibria that remain an equilibrium even if opponent(s) deviate to a best reply. In the unique best reply resistant equilibrium of the two-player game trade at the REE price occurs each time both traders receive contradicting private information.

We introduce a new zero-sum matrix game for modeling search in structured domains. In this game, one player tries to find a "bug" while the other tries to hide it. Both players exploit the structure of the "search" domain. Intuitively, this search game is a mathematical generalization of the well known binary search. The generalization is from searching over totally ordered sets to searching over more complex search domains such as trees, partial orders and general set systems. As there must be one row for every search strategy, and there are exponentially many ways to search even in very simple search domains, the game's matrix has exponential size ("space"). In this work we present two ways to reduce the space required to compute the Nash value (in pure strategies) of this game:

• First we show that a Nash equilibrium in pure strategies can be computed by using a backward induction on the matrices of each "part" or sub structure of the search domain. This can significantly reduce the space required to represent the game.

• Next, we show when general search domains can be represented as DAGs (Directed Acycliqe Graphs). As a result, the Nash equilibrium can be directly computed using the DAG. Consequently the space needed to compute the desired search strategy is reduced to O(n²) where n is the size of the search domain.

Determining the productivity of individual workers engaged in team production is difficult. Monitoring expenses may be high, or the observable output of the entire team may be some single product. One way to collect information about individual productivity is to observe how total output changes when the composition of the team changes. While some employers may explicitly shift workers from team to team for exactly this reason, the most common reasons for changes in team composition are at least partly voluntary: vacation time and sick days. In this paper, we develop a model of optimal absenteeism by employees which accounts for strategic interactions between employees. We assume the employer uses both observed changes in output and the strategies of the employees to form beliefs about a given worker's type. We argue that the model we develop is applicable to a variety of workplace situations where signaling models are not, because it allows a worker's decisions to provide information about other workers, as well as about himself.

A two-stage, two-person tournament is discussed, in which each player can influence the other one at the first stage by choosing help, sabotage or no action. At the second stage, the players choose effort to win the tournament. Helping and sabotaging have two effects — they influence the likelihood of winning (likelihood effect) and they determine the equilibrium efforts and, therefore, effort costs (cost effect). Depending on the interplay of the two effects, diverse types of equilibria are possible. In particular, if the cost effect dominates the likelihood effect (i.e., both players concentrate on minimizing effort costs), two asymmetric equilibria will coexist in which one player helps his opponent, whereas the other one chooses sabotage and vice versa.

Bergin and Lipman (1996) prove that equilibrium selection in the evolutionary dynamics of Kandori et al. (1993) and Young (1993), is not robust to variations in mutation rates across states. Specifically, a risk dominant equilibrium can be selected against if mutation rates are higher in its basin of attraction than elsewhere. Van Damme and Weibull (1998) model mutations as a compromise between payoff losses and control costs, which implies lower mutation rates in the risk dominant equilibrium. This paper argues that this result is not driven by control costs, but by players focusing on payoff losses when choosing mutation rates.