The formation of networks with transfers among players

We examine the formation of networks among a set of players whose payoffs depend on the structure of the network, when players may bargain by promising or demanding transfer payments when forming links. We vary three aspects of the game: (i) whether players can only make transfers to (and receive transfers from) players to whom they are directly linked, or whether they can also subsidize links that they are not directly involved in, (ii) whether or not transfers relating to a given link can be made contingent on the full resulting network or only on the link itself, and (iii) whether or not players can pay other players to refrain from forming links. We characterize the networks that are supported under these variations and show how each of the above aspects either accounts for a specific type of externality, or deals with the combinatorial nature of network payoffs.     

Stable lexicographic rules for shortest path games

For the class of shortest path games, we propose a family of new cost sharing rules satisfying core selection. These rules allocate shares according to some lexicographic preference relation. A computational procedure is provided. Our results relate to those of Tijs et al. (2011).     

Social optimality and cooperation in nonatomic congestion games

Congestion externalities may result in nonoptimal equilibria. For these to occur, it suffices that facilities differ in their fixed utilities or costs. As this paper shows, the only case in which equilibria are always socially optimal, regardless of the fixed components, in that in which the costs increase logarithmically with the size of the set of users. Therefore, achieving a socially optimal choice of facilities generally requires some form of external intervention or cooperation. For heterogeneous populations (in which the fixed utilities or costs vary across users as well as across facilities), this raises the question of utility or cost sharing. The sharing rule proposed in this paper is the Harsanyi transferable-utility value of the game—which is based on the users’ marginal contributions to the bargaining power of coalitions.     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

Fictitious play in 2×n games

It is known that every discrete-time fictitious play process approaches equilibrium in nondegenerate 2×2 games, and that every continuous-time fictitious play process approaches equilibrium in nondegenerate 2×2 and 2×3 games. It has also been conjectured that convergence to the set of equilibria holds generally for nondegenerate 2×n games. We give a simple geometric proof of this for the continuous-time process, and also extend the result to discrete-time fictitious play.     

Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.     

Self-tuning experience weighted attraction learning in games

Self-tuning experience weighted attraction (EWA) is a one-parameter theory of learning in games. It addresses a criticism that an earlier model (EWA) has too many parameters, by fixing some parameters at plausible values and replacing others with functions of experience so that they no longer need to be estimated. Consequently, it is econometrically simpler than the popular weighted fictitious play and reinforcement learning models. The functions of experience which replace free parameters “self-tune” over time, adjusting in a way that selects a sensible learning rule to capture subjects’ choice dynamics. For instance, the self-tuning EWA model can turn from a weighted fictitious play into an averaging reinforcement learning as subjects equilibrate and learn to ignore inferior foregone payoffs. The theory was tested on seven different games, and compared to the earlier parametric EWA model and a one-parameter stochastic equilibrium theory (QRE). Self-tuning EWA does as well as EWA in predicting behavior in new games, even though it has fewer parameters, and fits reliably better than the QRE equilibrium benchmark.     

Farsighted network formation

This paper studies a model of dynamic network formation when individuals are farsighted: players evaluate the desirability of a “current” move in terms of its consequences on the entire discounted stream of payoffs. We define a concept of equilibrium which takes into account farsighted behavior of agents and allows for limited cooperation amongst agents. We show that an equilibrium process of network formation exists. We also show that there are valuation structures in which no equilibrium strategy profile can sustain efficient networks. We then provide sufficient conditions under which the equilibrium process will yield efficient outcomes.     

A strategic implementation of the Average Tree solution for cycle-free graph games

In this note we provide a strategic implementation of the Average Tree solution for zero-monotonic cycle-free graph games. That is, we propose a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the average hierarchical outcome of the game. This mechanism takes into account that a player is only able to communicate with other players (i.e., to make proposals about a division of the surplus of cooperation) when they are connected in the graph.     

Strategic network formation through peering and service agreements

We introduce a game theoretic model of network formation in an effort to understand the complex system of business relationships between various Internet entities (e.g., Autonomous Systems, enterprise networks, residential customers). In our model we are given a network topology of nodes and links where the nodes act as the players of the game, and links represent potential contracts. Nodes wish to satisfy their demands, which earn potential revenues, but may have to pay their neighbors for links incident to them. We incorporate some of the qualities of Internet business relationships, including customer–provider and peering contracts. We show that every Nash equilibrium can be represented by a circulation flow of utility with certain constraints. This allows us to prove bounds on the prices of anarchy and stability. We also focus on the quality of equilibria achievable through centralized incentives.     

Bidding for surplus in network allocation problems

In this paper we study non-cooperative foundations of network allocation rules. We focus on three allocation rules: the Myerson value, the position value and the component-wise egalitarian solution. For any of these three rules we provide a characterization based on component efficiency and some balanced contribution property. Additionally, we present three mechanisms whose equilibrium payoffs are well defined and coincide with the three rules under consideration if the underlying value function is monotonic. Non-monotonic value functions are shown to deal with allocation rules applied to monotonic covers. The mechanisms are inspired by the implementation of the Shapley value by Pérez-Castrillo and Wettstein [Bidding for the surplus: a non-cooperative approach to the Shapley value, J. Econ. Theory 100 (2) (2001) 274-294].     

Self-control in peer groups

Social influences on self-control underlie both self-help groups and many peer interactions among youths. To understand these phenomena, we analyze how observing each other's behavior affects individuals’ ability to deal with their own impulses. These endogenous informational spillovers lead to either a unique “good news” equilibrium that ameliorates behavior, a unique “bad news equilibrium” that worsens it, or to the coexistence of both. A welfare analysis shows that people will find social interactions valuable only when they have enough confidence in their own and others’ ability to resist temptation. The ideal partner, however, is someone with a slightly worse self-control problem than one's own: this makes his successes more encouraging, and his failures less discouraging.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

An experimental investigation of overdissipation in the all pay auction

Pervasive overbidding represents a well-documented feature of all-pay auctions. Aggregate bids exceed Nash predictions in laboratory experiments, and individuals often submit bids that guarantee negative profits. This paper examines three factors that may reduce pervasive overbidding: (a) repetition (experience), (b) reputation (strangers vs. partners), and (c) active participation. Reputation and repetition reduce aggregate overdissipation, but they eliminate it only in conjunction with active participation.     

Minimal stable sets in tournaments

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.     

Approximate cores of games and economies with clubs

We introduce the framework of parameterized collections of games with and without sidepayments and provide three nonemptiness of approximate core theorems. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results. A fundamental new mathematical result, the partition-balancing effect of large numbers, which promises to have further applications, is contained in Appendix A.     

(Non-)existence and Scope of Nash Networks

For the connections model of strategic network formation, with two-way flow of information and without information decay, specific parameter configurations are given for which Nash networks do not exist. Moreover, existence and the scope of Nash network architectures are briefly discussed. We would like to thank two referees for helpful comments.     

Endowment effects in contests

We experimentally study overbidding in contests and find that overbidding is significantly higher when subjects are given a large per-experiment endowment rather than when the endowment is given per-period. Risk-aversion and non-monetary utility of winning can partially explain our findings.