International Journal of Game Theory最新文献

In an earlier paper published in this journal, Bauer (2023) claims to have constructed an auction format that maximizes buyers’ welfare. We note that the characterization of such a mechanism in Proposition 1 of Bauer (2023) is incomplete because it does not precisely specify the payment rule. Because of that, the discussion following this proposition is misleading and the mechanism proposed in the example is not incentive compatible. The complete characterization of the optimal mechanism is the one from Krishna and Perry (1998).

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.

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.

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.

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.

We extend the familiar shortest path problem by supposing that agents have demands over multiple periods. This potentially allows agents to combine their paths if their demands are complementary; for instance if one agent only needs a connection to the source in the summer while the other requires it only in the winter. We not only show that the resulting cost sharing problem always generates a totally balanced game, regardless of the number of agents and periods, the cost structure or the demand profile, but that all totally balanced games are representable as multi-period shortest path problems. We then exploit the fact that the model encompasses many well-studied problems to obtain or reobtain balancedness and total balancedness results for source-connection problems, assignment problems and minimum coloring problems.

An allocation rule is “withholding-proof" if no agent ever benefits from withholding some of the resources they own, their final bundle consisting of what the rule assigns to them together with whatever they withheld. It was known that on the “classical" domain of continuous, monotone, and convex preferences, no rule is efficient and withholding-proof (Postlewaite, Rev Econ Stud 46:255–262, 1979). We show that this disappointing news persists under the simultaneous imposition of the following three restrictions: (i) the domain only consists of classical and homothetic preferences; (iii) when an agent withholds some of their endowment, they only recover a percentage of what they withhold, no matter how close to 0 that percentage is; (iii) rules are required to satisfy any of the central punctual requirements of fairness, the individual-endowments lower bounds, no-envy in trades (adapted from Tinbergen, Redelijke Inkomensverdeling, Second Edition. N.D. DeGulden Pers, Haarlem, 1953, and Foley, Yale Economic Essays 7:45–98, 1967) and egalitarian-equivalence in trades (adapted from Pazner and Schmeidler, Quart J Econ 92:671–687, 1978 and Schmeidler and Vind, Econometrica 40:637–642, 1972).

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.

First, we suggest and discuss second-order versions of properties for solutions for TU games used to characterize the Banzhaf value, in particular, of standardness for two-player games, of the dummy player property, and of 2-efficiency. Then, we provide a number of characterizations of the Banzhaf value invoking the following properties: (i) [second-order standardness for two-player games or the second-order dummy player property] and 2-efficiency, (ii) standardness for one-player games, standardness for two-player games, and second-order 2-efficiency, (iii) standardness for one-player games, [second-order standardness for two-player games or the second-order dummy player property], and second-order 2-efficiency. These characterizations also work within the classes of simple games, of superadditive games, and of simple superadditive games.

Abstract

In order to understand if and how strategic resource allocation can constrain the structure of pair-wise competition outcomes in human competitions we introduce a new multiplayer resource allocation game, the Population Lotto Game. This new game allows agents to allocate their resources across a continuum of possible specializations. While this game allows non-transitive cycles between players, we show that the Nash equilibrium of the game also forms a hierarchical structure between discrete ‘leagues’ based on their different resource budgets, with potential sub-league structure and/or non-transitive cycles inside individual leagues. We provide an algorithm that can find a particular Nash equilibrium for any finite set of discrete sub-population sizes and budgets. Further, our algorithm finds the unique Nash equilibrium that remains stable for the subset of players with budgets below any threshold.