Problem Of Equilibrium Selection Research Articles

Local connectivity effects in learning and coordination dynamics in a two-layer network.

Anticoordination and chimera states occur in a two-layer model of learning and coordination dynamics in fully connected networks. Learning occurs in the intra-layer networks, while a coordination game is played in the inter-layer network. In this paper, we study the robustness of these states against local effects introduced by the local connectivity of random networks. We identify threshold values for the mean degree of the networks such that below these values, local effects prevent the existence of anticoordination and chimera states found in the fully connected setting. Local effects in the intra-layer learning network are more important than in the inter-layer network in preventing the existence of anticoordination states. The local connectivity of the intra- and inter-layer networks is important to avoid the occurrence of chimera states, but the local effects are stronger in the inter-layer coordination network than in the intra-layer learning network. We also study the effect of local connectivity on the problem of equilibrium selection in the asymmetric coordination game, showing that local effects favor the selection of the Pareto-dominant equilibrium in situations in which the risk-dominant equilibrium is selected in the fully connected network. In this case, again, the important local effects are those associated with the coordination dynamics inter-layer network. Indeed, lower average degree of the network connectivity between layers reduces the probability of achieving the risk-dominant strategy, favoring the Pareto-dominant equilibrium.

Decision Making and Games with Vector Outcomes

Abstract In this paper, we study decision making and games with vector outcomes. We provide a general framework where outcomes lie in a real topological vector space and the decision maker’s preferences over outcomes are described by a preference cone, which is defined as a convex cone satisfying a continuity axiom. Further, we define a notion of utility representation and introduce a duality between outcomes and utilities. We provide conditions under which a preference cone is represented by a utility and is the dual of a set of utilities. We formulate a decision-making problem with vector outcomes and study optimal choices. We also consider games with vector outcomes and characterize the set of equilibria. Lastly, we discuss the problem of equilibrium selection based on our characterization.

Equilibrium Selection in Second-Price Common-Value Auctions

This paper considers the problem of equilibrium selection in a second-price auction with two bidders. We show that for each ex post equilibrium in continuous and undominated strategies of the auction, a sequence of almost common-value auctions can be constructed such that each of them possesses a unique undominated and continuous equilibrium and the corresponding sequence of equilibria converges to that ex post equilibrium. Therefore, no equilibrium selection of this model based on perturbations seems to be more convincing than others.

Deterministic equations for stochastic spatial evolutionary games

Spatial evolutionary games model individuals playing a game with their neighbors in a spatial domain and describe the time evolution of the strategy profile of individuals over space. We derive integro-differential equations as deterministic approximations of strategy revision stochastic processes. These equations generalize the existing ordinary differential equations such as replicator dynamics and provide powerful tools for investigating the problem of equilibrium selection. Deterministic equations allow the identification of many interesting features of the evolution of a population’s strategy profiles, including traveling front solutions and pattern formation.

Risk, rationality, and resilience

Improving our ability to cope with large risks is one of the key challenges for humankind in this century. This article outlines a research program in this perspective. Starting with a concrete example of a relatively small disaster, it questions simplistic ideas of rationality. It then proposes a fresh look at the concepts of probability and utility in the context of socio-ecological systems. This leads first to an emphasis on the problem of equilibrium selection, and then to a distinction between three kinds of resilience that matter both for theory and practice of risk management. They can be investigated by paying attention to the transitions into and out of actual disasters.

Stationary points and equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game-theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path following methods to find a stationary point and illustrate such methods by an example. Finally, we discuss some refinements of stationary points and their application to solve the problem of equilibrium selection.

Eductive expectations coordination on deterministic cycles in an economy with identical fundamentals

We study expectations coordination on a deterministic cycle of period 2 by an eductive approach in which agents are concerned with forecasting the forecasts of others. This approach is grounded in some Common Knowledge assumptions. We use this approach to discuss the problem of equilibrium selection between the stationary state and a cycle of period 2. We prove that locally eductively stable cycles of period 2 can exist if agents have stationary beliefs.

Waiting for an echo: the revolution in general equilibrium theory and the paralysis in introductory economics

The current framework for the introductory microeconomics course is predicated on the Invisible Hand lessons of mid-twentieth century General Equilibrium Theory. During the final decades of the century, however, the theory changed. Proofs of the path-dependent instability of general equilibrium, the multiplicity of equilibria and the problem of equilibrium selection, and the failure of asymptotic convergence to the properties of equilibrium (The General Theory of the Second Best) provided a sweeping disconfirmation of the Invisible Hand. This paper argues that these topics are fully teachable, even at the principles level, and that they point toward a new framework for the curriculum in which institutions can reclaim much of the explanatory space now occupied by market analysis.

Equilibrium selection in a nonlinear duopoly game with adaptive expectations

We analyze a nonlinear discrete time Cournot duopoly game, where players have adaptive expectations. The evolution of expected outputs over time is generated by the iteration of a noninvertible two-dimensional map. The long-run behavior is characterized by multistability, that is, the presence of coexisting stable consistent beliefs, which correspond to Nash equilibria in the quantity space. Hence, a problem of equilibrium selection arises and the long run outcome strongly depends on the choice of the players’ initial beliefs. We analyze the basins of attraction and their qualitative changes as the model parameters vary. We illustrate that the basins might be nonconnected sets and reveal the mechanism which is responsible for this often-neglected kind of complexity. The analysis of the global bifurcations which cause qualitative changes in the topological structure of the basins is carried out by the method of critical curves.

Demonstrating the Possibility of Pareto Inferior Nash Equilibria

(2000). Demonstrating the Possibility of Pareto Inferior Nash Equilibria. The Journal of Economic Education: Vol. 31, No. 4, pp. 358-362.

Credible Proposals in Communication Games

We present a nonequilibrium theory for simple communication games and use this theory to construct a new way of examining the problem of equilibrium selection in signaling and communication games. Our approach differs from the current literature in that the beliefs of the receiver after receiving an unexpected message are independent of the equilibrium payoffs. This property makes our approach immune to criticisms of conventional refinements, such as the Stiglitz critique.Journal of Economic LiteratureClassification Number: C72.

Introspection and equilibrium selection in 2 � 2 matrix games

Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite simple games, as 2 × 2 games with two strict Nash equilibria.