Global Coalitional Games

Global coalitional games are TU cooperative games intended to model situations where the worth of coalitions varies across different partitions of the players. Formally, they are real-valued functions whose domain is the direct product of the subset lattice and the lattice of partitions of a finite player set. Therefore, the dimension of the associated vector space grows dramatically fast with the cardinality of the player set, inducing flexibility as well as complexity. Accordingly, some reasonable restrictions that reduce such a dimension are considered. The solution concepts associated with the Shapley value and the core are studied for the general (i.e., unrestricted) case.lattice, lattice function, coalition, partition, Shapley value, core

Heterogeneity and Uniqueness in Interaction Games

Incomplete information games, local interaction games and random matching games are all special cases of a general class of interaction games (Morris (1997)). In this paper, we use this equivalence to present a unified treatment of arguments generating uniqueness in games with strategic complementarities by introducing heterogeneity in these different settings. We also report on the relation between local and global heterogeneity, on the role of strategic multipliers and on purification in the three types of interaction game.Heterogeneity, Uniqueness, Global games

Network Structure in a Link-formation Game: An Experimental Study

Network formation is frequently modeled using link-formation games and typically present a multiplicity of Nash equilibria. Cooperative refinements - such as strong or coalitional proof Nash equilibria - have been the standard tool used for equilibrium selection in these games. Non-cooperative refinements derived from the theory of global games have shown also that, for a class of payoff functions, multiplicity of equilibria disappears when the game is perturbed by introducing small amounts of incomplete information. We conducted a laboratory study evaluating the predictive power of each of these refinements in an illustrative link-formation game. Compared with cooperative game solutions, the global game approach did significantly better at predicting the strategies played by individuals in the experiment.Networks, global games, cooperative games, equilibrium selection, experimental economics

Some Notes on Learning in Games with Strategic Complementarities

Fictitious play is the classical myopic learning process, and games with strategic complementarities are an important class of games including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond dominance solvable games, global convergence has only been established for games with strategic complementarities and diminishing marginal returns (Krishna, 1992, HBSWorking Paper 92-073). This result is known to depend critically on the assumption of a tie-breaking rule. We show that restricting the analysis to nondegenerate games allows us to drop this assumption. More importantly, an ordinal version of strategic complementarities turns out to suffice. As a byproduct, we also obtain global convergence in generalized ordinal potential games with diminishing marginal returns.Fictitious Play, Learning Process, Strategic Complementarities, Supermodular Games

Continuous-time integral dynamics for Aggregative Game equilibrium seeking

In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results

Games of strategic complementarities: An application to bayesian games

Games of strategic complementarities are those in which any player increases his action in response to an increase in the level of actions of rivals. This paper provides an introduction to the theory of games of strategic complementarities, considers Bayesian games, and provides an application to global games.Strategic complementarities; games theory;

Portfolio Construction in Global Financial Markets

This paper presents a classroom simulation that can be used to introduce the concepts of portfolio management and asset allocation in the presence of global markets. While there are portfolio management games and stock trading games that are designed to cover an entire semester, this simulation provides a single period introduction to portfolio management. The simulation also creates an environment in which students discover how exchange rate volatility can affect investment returns of global funds.

Equilibrium Selection in Static and Dynamic Entry Games

We experimentally examine equilibrium refinements in static and dynamic binary choice games of complete information with strategic complementarities known as “entry†games. Our aim is to assess the predictive power of two different equilibrium selection principles. In static entry games, we test the theory of global games as an equilibrium selection device. This theory posits that players play games of complete information as if they were playing a related global game of incomplete information. In dynamic entry games, individuals decide not only whether to enter but also when to enter. Once entry occurs it is irreversible. The number of people who have already entered is part of the state description, and individuals can condition their decisions on that information. If the state variable does not indicate that entry is dominated, the efficient subgame perfect equilibrium prediction calls for all players to enter. Further, if there is a cost of delay, entry should occur immediately, thereby eliminating the coordination problem. This subgame perfect entry threshold in the dynamic game will generally differ from the global game threshold in static versions of the same entry game. Nevertheless, our experimental findings suggest that observed entry thresholds in both static and dynamic versions of the same entry game are surprisingly similar. The mean entry threshold in the static game lies below the global game equilibrium threshold while the mean entry threshold in the dynamic game lies above the efficient subgame perfect equilibrium threshold. An important implication of this finding is that if one were to observe only the value of the state variable and the number of people who enter by the end of the game one could not determine whether the static or the dynamic game had been played.