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Abstract: Abstract A group of agents are waiting to be served in a facility. Each server in the facility can serve only one agent at a time and agents differ in their cost-types. For this queueing problem, we are interested in finding the order in which to serve agents and the corresponding monetary transfers for the agents. In the standard queueing problem, each agent’s waiting cost is assumed to be constant per unit of time. In this paper, we allow the waiting cost of each agent to depend on the cost-type of each agent and the position assigned to be served. Furthermore, this function is assumed to be supermodular with respect to the cost-type and the position, and non-decreasing with respect to each argument. Our “positional queueing problem” generalizes the queueing problem with multiple parallel servers (Chun and Heo in Int J Econ Theory 4:299–315, 2008) as well as the position allocation problem (Essen and Wooders in J Econ Theory 196:105315, 2021). By applying the Shapley value to the problem, we obtain the optimistic and the pessimistic Shapley rules which are extensions of the minimal (Maniquet in J Econ Theory 109:90–103, 2003) and the maximal (Chun in Math Soc Scie 51:171–181, 2006) transfer rules of the standard queueing problem. We also present axiomatic characterizations of the two rules. The optimistic Shapley rule is the only rule satisfying efficiency and Pareto indifference together with (1) equal treatment of equals and independence of larger cost-types or (2) the identical cost-types lower bound, negative cost-type monotonicity, and last-agent equal responsibility. On the other hand, the pessimistic Shapley rule is the only rule satisfying efficiency and Pareto indifference together with (1) equal treatment of equals and independence of smaller cost-types or (2) the identical cost-types lower bound, positive cost-type monotonicity, and first-agent equal responsibility under constant completion time. PubDate: 2024-07-04

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Abstract: Abstract We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite N-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space of real symmetric matrices. For semidefinite two-player zero-sum games, we show that the optimal strategies can be computed by semidefinite programming. Furthermore, we show that two-player semidefinite zero-sum games are almost equivalent to semidefinite programming, generalizing Dantzig’s result on the almost equivalence of bimatrix games and linear programming. For general two-player semidefinite games, we prove a spectrahedral characterization of the Nash equilibria. Moreover, we give constructions of semidefinite games with many Nash equilibria. In particular, we give a construction of semidefinite games whose number of connected components of Nash equilibria exceeds the long standing best known construction for many Nash equilibria in bimatrix games, which was presented by von Stengel in 1999. PubDate: 2024-06-20

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Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

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Abstract: Abstract In this paper we study a non-cooperative sequential equilibrium concept, namely the Stackelberg–Nash equilibrium, in a game in which heterogeneous atomic traders interact in interrelated markets. To this end, we consider a two-stage quantity setting strategic market game with a finite number of traders. Within this framework, we define a Stackelberg–Nash equilibrium. Then, we show existence and local uniqueness of a Stackelberg–Nash equilibrium with trade. To this end, we use a differentiable approach: the vector mapping which determines the strategies of followers is a smooth local diffeomorphism, and the set of Stackelberg–Nash equilibria with trade is discrete, i.e., the interior equilibria of the game are locally unique. We also compare through examples the sequential and the simultaneous moves games. A striking difference is that exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. PubDate: 2024-06-01

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Abstract: Abstract This paper studies multilateral trading problems in which agents’ valuations for items are interdependent. Assuming that each agent’s information has a greater marginal effect on her own valuation than on the other agents’ valuations, the paper identifies a necessary and sufficient condition for the existence of trading mechanisms satisfying efficiency, ex-post incentive compatibility, ex-post individual rationality, and ex-post budget balance. The paper presents a trading mechanism that satisfies the four properties when the necessary and sufficient condition holds and shows that this mechanism maximizes the ex-post budget surplus among all efficient, ex-post incentive compatible, and ex-post individually rational trading mechanisms. The paper examines an environment where each agent can possess at most one unit of an item, and her information about the item is one-dimensional. It then extends the results to two general environments: the multiple units environment and the multidimensional information environment. PubDate: 2024-06-01

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Abstract: Abstract The Lowest Unique Positive Integer game, a.k.a. Limbo, is among the simplest games that can be played by any number of players and has a nontrivial strategic component. Players independently pick positive integers, and the winner is the player that picks the smallest number nobody else picks. The Nash equilibrium for this game is a mixed strategy, \((p(1),p(2),\ldots )\) , where p(k) is the probability you pick k. A recursion for the Nash equilibrium has been previously worked out in the case where the number of players is Poisson distributed, an assumption that can be justified when there is a large pool of potential players. Here, we summarize previous results and prove that as the (expected) number of players, n, goes to infinity, a properly scaled version of the Nash equilibrium random variable converges in distribution to a Unif(0, 1) random variable. The result implies that for large n, players should choose a number uniformly between 1 and \(\phi _n \sim O(n/\ln (n))\) . Convergence to the uniform is rather slow, so we also investigate a continuous analog of the Nash equilibrium using a differential equation derived from the recursion. The resulting approximation is unexpectedly accurate and is interesting in its own right. Studying the differential equation yields some useful analytical results, including a precise expression for \(\phi _n\) , and efficient ways to sample from the continuous approximation. PubDate: 2024-06-01

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Abstract: Abstract This paper provides a new characterization of belief consistency in extensive games. We show that all consistent assessments are supported by sequences of strategy profiles with the property that all actions with vanishing probability are played according to power functions of the sequence index. The result makes it simpler to prove or disprove that a given assessment is consistent, facilitating the use of sequential equilibria. PubDate: 2024-06-01

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Abstract: Abstract A seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either good. The value of the bundle and the ratio are the agent’s private information. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price or a posted price mechanism for a class of distributions. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio are independently distributed. PubDate: 2024-06-01

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Abstract: Abstract We introduce a new class of values for coalitional games: the coalition-weighted Shapley values. Weights can be assigned to coalitions, not just to players, and zero-weights are admissible. The Shapley value belongs to this class. Coalition-weighted Shapley values recommend for each game the allocation defined by the Shapley value of a weighted game obtained as a linear convex combination of the associated marginal games. Coalition-weighted Shapley values are random order values and Harsanyi values. Positively weighted Shapley values and weighted Shapley values can be seen as the limit of a sequence of iterated coalition-weighted Shapley values. We provide axiomatic characterizations of coalition-weighted Shapley values through properties that do not involve the weights. Finally, we discuss how to extend our model to include exogenous coalition structures as in the hierarchical and Owen values. PubDate: 2024-06-01

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Abstract: Abstract We study the endogenous participation problem when bidders are characterized by a two-dimensional private information on valuations and participation costs in first-price auctions. Bidders participate whenever their private costs are less than or equal to the expected revenue from participating. We show that there always exists an equilibrium in this general setting with two-dimensional types of ex-ante heterogeneous bidders. When bidders are ex-ante homogeneous, there is a unique symmetric equilibrium, but asymmetric equilibria may also exist. We provide conditions under which the equilibrium is unique (not only among symmetric ones). In the symmetric equilibrium, we show that the equilibrium cutoff of participation costs described above which bidders never participate, is lower when the distribution of participation costs is first-order stochastically dominated. PubDate: 2024-06-01

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Abstract: Abstract We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u, v) is a move whenever (v, u) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n-person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players. PubDate: 2024-06-01

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Abstract: Abstract This paper considers pure strategy Nash equilibria of non-cooperative legislative bargaining models. In contrast to existing legislative bargaining models, we derive legislators behavior from stochastic utility maximization. This approach allows us to prove the existence of a stationary Pure Local and Global Nash Equilibrium under rather general settings. The mathematical proof is based on a fixed point argument, which can also be used as a numerical method to determine an equilibrium. We characterize the equilibrium outcome as a lottery of legislators’ proposals and prove a Mean Voter Theorem, i.e., proposals result dimension-by-dimension as a weighted mean of legislators’ ideal points and are Pareto-optimal. Based on a simple example, we illustrate different logic of our model compared to mixed strategy equilibrium of the legislative bargaining model suggested by Banks and Duggan (Am Polit Sci Rev 94(1):73–88. https://doi.org/10.2307/2586381, 2000). PubDate: 2024-06-01

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Abstract: Abstract This paper studies a Bayesian persuasion game in which a receiver can receive signals from two senders. We study under what circumstances the competition between senders induces them to fully disclose all of the signals available. We find that if the senders’ preferences are such that they are opposite to the same degree across states (to be made precise in the paper), full disclosure is the only equilibrium outcome of the game. Furthermore, we find that the above condition on the senders’ preferences is also necessary if we require that full disclosure be the only equilibrium outcome for any receiver’s utility and any information environment. PubDate: 2024-06-01

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Abstract: Abstract We define a new impartial combinatorial game, FLAG COLORING, based on flood filling, and find some values and outcome classes for some game positions. We then generalize FLAG COLORING to a graph game, re-imagining the game on two colors as an edge-reduction game on graphs, and find values for many positions represented as graph families on two colors. We demonstrate that the generalized game is PSPACE-complete for two or more colors via a reduction from AVOID TRUE. Finally, remaining open problems are discussed. PubDate: 2024-05-24

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Abstract: Abstract We present a test of the two most established reciprocity models, an intention factor model and a reference value model. We test characteristic elements of each model in a series of twelve mini-ultimatum games. Results from online experiments show major differences between actual behavior and predictions of both models: the distance of actual offers to the proposed reference value provides a poor measure for the kindness of offers, while a comparison of offers with extreme offers as suggested by the intention factor model makes offers indiscriminable in richer settings. We discuss possible combinations of both models better describing our observations. PubDate: 2024-05-21

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Abstract: Abstract We examine infinite horizon decision problems with arbitrary bounded payoff functions in which the decision maker uses finitely additive behavioral strategies. Since we only assume that the payoff function is bounded, it is well-known that these behavioral strategies generally do not induce unambiguously defined expected payoffs. Consequently, it is not clear how to compare behavioral strategies and define optimality. We address this problem by finding conditions on the payoff function that guarantee an unambiguous expected payoff regardless of which behavioral strategy the decision maker uses. To this end, we systematically consider various alternatives proposed in the literature on how to define the finitely additive probability measure on the set of infinite plays induced by a behavioral strategy. PubDate: 2024-05-14

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Abstract: Abstract In this study, we concern with a class linear quadratic (LQ, for short) N-person differential games with time inconsistency, where the time inconsistency arises from non-exponential discount function. The notions of closed-loop and open-loop equilibrium strategy are introduced. We establish the equivalent relationship between time-inconsistent differential game problems, forward-backward type differential equations, and Riccati type differential equations in the framework of closed-loop and open-loop equilibrium, respectively. We provide an example of time-inconsistent differential games from which we find a time-consistent equilibrium strategy. PubDate: 2024-04-18 DOI: 10.1007/s00182-024-00895-2

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Abstract: Abstract We develop a unified derivation of asymmetric pure strategy equilibria and their optimality in the canonical common interest voting model of Austen-Smith and Banks (Am Polit Sci Rev 90(1):34–45, 1996). We also study the relationship between the most efficient equilibria, which have a remarkably simple and intuitive structure, and the symmetric mixed strategy equilibrium that has been commonly studied in the literature. In particular, while the efficiency in the symmetric mixed strategy equilibrium under unanimity rule is known to be decreasing in the number of voters, the efficiency does not depend on the number of voters above a threshold in the most efficient equilibria. PubDate: 2024-03-15 DOI: 10.1007/s00182-024-00886-3

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Abstract: Abstract We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is minimally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts. PubDate: 2024-03-10 DOI: 10.1007/s00182-024-00887-2