Invitation Games: An Experimental Approach to Coalition Formation

This paper studies how to form an efficient coalition—a group of people. More specifically, we compare two mechanisms for forming a coalition by running a laboratory experiment and reveal which mechanism leads to higher social surplus. In one setting, we invite the subjects to join a meeting simultaneously, so they cannot know the other subjects’ decisions. In the other setting, we ask them sequentially, which allows each subject to know his or her predecessor’s choice. Those who decide to join the meeting form a coalition and earn payoffs according to their actions and individual preferences. As a result, we obtain the following findings. First, the sequential mechanism induces higher social surplus than the simultaneous mechanism. Second, most subjects make choices consistent with the subgame-perfect Nash equilibrium in the sequential setting and choose the dominant strategy in the simultaneous setting, when a dominant strategy exists. Finally, when the subjects need to look further ahead to make a theoretically rational choice, they are more likely to fail to choose rationally.

An axiomatic and non-cooperative approach to the multi-step Shapley value

Inspired by the two-step Shapley value, in this paper we introduce and axiomatize the multi-step Shapley value for cooperative games with levels structures. Moreover, we design a multi-step bidding mechanism, which implements the value strategically in subgame perfect Nash equilibrium for superadditve games.

Efficient multi-period distribution mechanism for the innovation investment system under uncertainty

In this paper, we study the problem of a venture investor who distributes the budget between several innovation projects under conditions of uncertainty. A common method for solving this problem is through bilateral negotiations with the external evaluation of projects. However, the effectiveness almost entirely depends on the evaluation quality, but external evaluation seldom reduces the knowledge asymmetry for innovation projects. We propose an iterative revelation mechanism for this problem when the investor sequentially offers possible allocations of the limited budget in the form of threshold dividing questions. The binary choices of innovators serve as a signal of internal estimates of the project implementation costs. Under perfect information, such a mechanism, regardless of the method for determining budget allocations, always produces an effective allocation in subgame-perfect Nash equilibrium. Under uncertainty, the method of offering distribution options matters – the optimal solution is found under the English auction class of mechanisms. In an efficient iterative allocation mechanism for innovation investment, the investor proposes a new allocation of the budget each round until an efficient allocation is achieved. The proposed mechanism does not necessarily need to identify the exact minimum budgets for each innovator. Another advantage of the proposed mechanism is the ability to use different processes for organizing rounds.

Group cooperation against a hegemon

In this paper, I study the ability of a group of citizens to cooperate against a hegemon in a repeated contest game and where group members and the hegemon have different valuations of the prize. I first consider that group members use grim trigger strategies (GTSs) to support cooperative behavior and show that full cooperation within the group is more easily sustained as a stationary subgame perfect (Nash) equilibrium (SSPE) as either group size or the heterogeneity in the valuation of the prize increases. In turn, I show that full cooperation within the group can also be sustained as a weakly renegotiation-proof equilibrium (WRPE). However, an increase in group size makes it more difficult to sustain within-group cooperation, but an increase in the relative valuation of the prize by group members still facilitates group cooperation.

A Note on Stabilizing Cooperation in the Centipede Game

In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed.

Revealed Preference Implications of Backward Induction and Subgame Perfection

Consider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

Optimal eco-labeling strategy with imperfectly informed consumers

Purpose The purpose of this paper is to find the optimal environmental quality criteria for a strategic eco-labeling authority with three objectives (i.e. maximizing the aggregate environmental quality, maximizing the industry profit and maximizing the social welfare). Particularly, the authors investigate how the existence of imperfectly informed consumers affects labeling criteria determination and competition among firms. Design/methodology/approach A game-theoretic modeling approach was adopted in this paper. A three-stage sequential game was modeled and backward induction was used to solve for a subgame perfect Nash equilibrium. To investigate the impacts of the existence of imperfectly informed consumers, the equilibrium, if all consumers are perfectly informed of the eco-label, was studied as a benchmark. Findings A more strict eco-labeling criterion improves revenues for both the labeled and unlabeled firms. It is interesting to find that the eco-labeling criteria to maximize industry profits are stricter than the criteria to maximize social welfare. Moreover, when the fraction of imperfectly informed consumers increases, the eco-labeling criteria to maximize aggregate environmental quality or industry profits will be more strict, while the criteria to maximize the social welfare will be looser. Originality/value The authors analyze the equilibrium strategies for firms against the eco-labeling criteria certified by authority with different objectives. The obtained optimal labeling strategies could provide insightful guidelines for the certifying authority to select the best suitable labeling criteria to achieve its goals.

Investment on human capital in a dynamic contest model

Although most contest games are modeled in such a way that the outcome depends only on the efforts exerted by the contestants, what is arguably more important is the contestants’ effective efforts which may be influenced also by their ability, human capital, strength, etc. In this paper, we investigate an extensive model including such an effectiveness parameter and analyze the optimal investment behavior in a dynamic conflict framework. At each period, two contestants compete for a common prize by choosing contest efforts and investment levels. Each contestant’s investment accumulates as his/her human capital which depreciates through time. Who wins the component contest at a particular period is determined by the contestants’ effective efforts, defined as increasing functions of their efforts and human capitals. Following the analysis of subgame perfect Nash equilibrium in a two-period model and of open-loop equilibrium in an infinite-horizon model, we provide intuitive comparative static results.

Design for Repair: A Game Between Manufacturer and Independent Repair Service Provider

Design for ease-of-repair is an efficient solution to effectively use resources by extending the lifespan of products. However, designing a repairable product may not be necessarily an economically viable solution for manufacturers. Repairable products enable independent repair businesses to compete with original manufacturers on offering repair services. On the other hand, although designing a less repairable product may dissuade competition, it increases the cost of repair for manufacturers at the same time, in addition to decreasing consumers’ satisfaction. In this paper, a game-theoretic model is developed to represent the competition between a manufacturer acting as a leader, and a coalition of independent repair service providers acting as a follower. The subgame perfect Nash equilibrium is derived, representing the optimal prices for repair services offered by the two service-providers based on the level of repairability. In addition, based on the information extracted from a repair-related survey, we provide insights about consumers’ attitudes towards repairability of products to help manufacturers make better design decisions.