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Suppose identical jobs need to be processed by a single processor. Processing is carried out one job after the other, in batches, and jobs are released only when their entire batch is done. Each job is held by an agent, who tries to minimize costs. The cost of an individual job is linear in two terms: a congestion cost, dependent on the size of the batch, and a lateness cost, dependent also on the number of jobs preceding the batch. The agents need to decide on the sequential index of the batch they ascribe to. This decision problem is stated as a non-cooperative game, with applications both in ride sharing and in queues in which the server must never be idle. We derive its (mixed) symmetric equilibrium, which always exists, and its pure non-symmetric equilibrium, when it exists. The corresponding social optimization problem is solved as well, leading, in the mixed symmetric case, to an explicit formula for the price of anarchy.

This article presents a new approach to analyze the equilibrium set of symmetric, differentiable games by separating multiple symmetric equilibria and asymmetric equilibria. This separation allows the investigation of, for example, how various parameter constellations affect the scope for multiple symmetric or asymmetric equilibria, or how the equilibrium set depends on the nature of the strategies. The approach is particularly helpful in applications because (i) it allows the complexity of the uniqueness problem to be reduced to a two-player game, (ii) boundary conditions are less critical compared to standard procedures, and (iii) best replies need not be everywhere differentiable. The usefulness of the separation approach is illustrated with several examples, including an application to asymmetric games and to a two-dimensional price-information game.

We consider a version of the Battle of the Sexes with private information and allow cheap talk regarding the players’ types before the game. We show that a desirable type-coordination property is achieved at the unique fully revealing symmetric equilibrium (when it exists). Type-coordination is also obtained in a partially revealing equilibrium that exists when the fully revealing equilibrium does not. We further prove that truthfully revealed messages, followed by actions that depend meaningfully on these messages, are not equilibrium profiles with one-sided cheap talk. Finally, fully revealing equilibria do not exist under sequential communication either.

Research on the spatial aspects of economic activity has flourished over the past decade due to the emergence of new theory, new data, and an intense interest on the part of policymakers, especially in Europe but increasingly in North America and elsewhere as well. However, these efforts--collectively known as the \"new economic geography\"--have devoted little attention to the policy implications of the new theory. Economic Geography and Public Policyfills the gap by illustrating many new policy insights economic geography models can offer to the realm of theoretical policy analysis. Focusing primarily on trade policy, tax policy, and regional policy, Richard Baldwin and coauthors show how these models can be used to make sense of real-world situations. The book not only provides much fresh analysis but also synthesizes insights from the existing literature. The authors begin by presenting and analyzing the widest range of new economic geography models to date. From there they proceed to examine previously unaddressed welfare and policy issues including, in separate sections, trade policy (unilateral, reciprocal, and preferential), tax policy (agglomeration with taxes and public goods, tax competition and agglomeration), and regional policy (infrastructure policies and the political economy of regional subsidies). A well-organized, engaging narrative that progresses smoothly from fundamentals to more complex material,Economic Geography and Public Policyis essential reading for graduate students, researchers, and policymakers seeking new approaches to spatial policy issues.

In an m-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player k in an m-person symmetric game is k-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the m-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

In this paper, we establish an existence theorem by using the Kakutani-Fan-Glicksberg fixed-point theorem for a symmetric generalized quasi-variational inclusion problem in real locally convex Hausdorff topological vector spaces. Moreover, the closedness of the solution set for this problem is obtained. As special cases, we also derive the existence results for symmetric weak and strong quasi-equilibrium problems. The results presented in the paper improve and extend the main results in the literature. MSC: 90B20, 49J40.

This paper analyzes the dynamics of entry and adjustment that underlies the process leading to the tragedy of the commons under two scenarios, one in which the users only react ex post to the entry of other users and the other in which the users anticipate and proact to such entry. The key to our analysis is the logic of entry based on the devaluation cost, which explains (1) why entry takes place when the incumbent users are in temporary equilibrium, (2) how this equilibrium shifts sequentially with the entry of new users, (3) why such equilibria resemble either the Cournot-Nash equilibrium of a static game or the Stackelberg type equilibrium of a dynamic game depending on the reactive or the proactive nature of the users, (4) why the stocks owned by the users in the proactive case depend on the order of entry and remain unchanged once determined at the point of entry. The speed of depletion, cumulative profits of the users, and the distribution pattern of the ownership differ significantly between the two scenarios. Our theory also explains why and how duopoly and oligopoly emerge through the process of entry and adjustment and acquire different equilibrium features.

The \"generalized second-price auction\" is widely employed to sell internet advertising positions and has many equilibria. Analysis of this auction has assumed that myopic players commonly know each others' position values, and that the resulting equilibrium play is \"locally envy-free\". Here, I argue that the appropriate refinement of Nash equilibrium for this setting is evolutionary stability, and show that it implies that an equilibrium is locally envy-free if the whole population of players bids in each auction and the set of possible bids is not too coarse. However, not all locally envy-free equilibria are evolutionarily stable in this case, as I show by example for the popular Vickrey-Clarke-Groves outcome. The existence of evolutionarily stable equilibrium is established when one position is auctioned, as well as for two positions and a large number of bidders.

We study a 2-player stochastic differential game of lobbying. Players invest in lobbying activities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We consider the Nash symmetric game where players face the same cost and extract symmetric payoffs, and we solve for Markov Perfect Equilibria (MPE) in the class of affine functions. First, we prove a general sufficient (catching up) optimality condition for two-player stochastic games with uncertainty driven by Wiener processes. Second, we prove that the number and nature of MPE depend on the extent of uncertainty (i.e. the variance of the Wiener processes). In particular, we prove that while a symmetric MPE always exists, two asymmetric MPE emerge if and only if uncertainty is large enough. Third, we study the stochastic stability of all the equilibria. We notably find, that the state converges to a stationary invariant distribution under asymmetric MPE. Fourth, we study the implications for rent dissipation asymptotically and compare the outcomes of symmetric vs asymmetric MPE in this respect, ultimately enhancing again the role of uncertainty.

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan’s lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maximal element lemma, while it is useless for proving the main theorem of this paper. Our results can be viewed as an extension and improvement of the main results obtained by Farajzadeh (Filomat 29(9):2097-2105, 2015 ) and some corresponding results that appeared in this area by relaxing the lower semicontinuity, quasiconvexity on the mappings and being nontrivial of the dual cones. Finally, some examples are given to support the main results.