http://rcer.econ.rochester.edu/RCERPAPERS/rcer_578.pdf

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: an update

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved. Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players. This interplay between optimisation and allocation is the main subject of the area of operations research games. It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.

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Operations Research Games: a Survey

We start with giving an axiomatic characterization of the Nash equilibrium (NE) correspondence in terms of consistency, converse consistency and one-person rationality. Then axiomatizations are given of the strong NE correspondence, the coalition-proof NE correspondence and the semi-strong NE. In all these characterizations consistency and suitable variants of converse consistency play a role. Finally, the dominant NE correspondence is characterized. We also indicate how to generalize our results to Bayesian and extensive games. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item (This abstract was borrowed from another version of this item.)

The consistency principle for games in strategic form

Many real-world decision problems are inherently multi-objective in nature and concern multiple actors, making multi-objective multi-agent systems a key domain to study. We argue that trade-offs between conflicting objective functions should be analysed on the basis of the utility that these trade-offs have for the users of a system. We develop a new taxonomy which classifies multi-objective multi-agent decision making settings, on the basis of the reward structures and utility functions. We analyse which solution concepts apply to the different settings in our taxonomy, which allows us to offer a structured view of the field and identify promising directions for future research.

Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey

Selecting permit allocation rules for agricultural pollution control: a bargaining solution

Pareto equilibria in multicriteria games can be computed as the Nash equilibria of scalarized games, obtained by assigning weights to the separate criteria of a player. To analysts, these weights are usually unknown. This paper therefore proposes ideal equilibria, strategy profiles that are robust against unilateral deviations of the players no matter what importance is assigned to the criteria. Existence of ideal equilibria is not guaranteed, but several desirable properties are provided. As opposed to the computation of other solution concepts in noncooperative multicriteria games, the computation of the set of ideal equilibria is relatively simple: an exact upper bound for the number of scalarizations is the maximum number of criteria of the players. The ideal equilibrium concept is axiomatized. Moreover, the final section provides a non-trivial class of multicriteria games in which ideal equilibria exist, by establishing a link to the literature on potential games.

Ideal equilibria in noncooperative multicriteria games

A class of cooperative games arising from shortest path problems is defined. These shortest path games are totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; first, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs into account by considering the costs of the second best alternative and that rewards players who are crucial to the construction of the shortest path. The core and the bargaining sets of Davis-Maschler and Mas-Colell are shown to coincide. Finally, noncooperative games arising from shortest path problems are introduced, in which players make bids or claims on paths. The core allocations of the cooperative shortest path game coincide with the payoff vectors in the strong Nash equilibria of the associated noncooperative shortest path game.

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Cost allocation in shortest path games

Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition reflecting the decreasing marginal contribution of non-clan members to growing coalitions. This decreasing marginal contribution is incorporated in the notion of a bi-monotonic allocation scheme, where the value of each coalition is divided over its members in such a way that the clan members receive a higher, and the non-clan members a lower share as the coalitions grow larger. Each core element of a total clan game can be extended to both a population monotonic and a bi-monotonic allocation scheme. In total clan games where the clan consists of a single member (the so-called big boss) the use of the nucleolus as an allocation mechanism gives rise to a bi-monotonic allocation scheme.

/pdf/monotonic-allocation-schemes-in-clan-games-r2r68f24xz.pdf

Monotonic Allocation Schemes in Clan Games

The USA Bankruptcy Code legislates the bankruptcy of firms. Any allocation mechanism that is legal according to the Bankruptcy Code is necessarily population monotonic. Bankruptcy rules yielding a population monotonic allocation scheme in the associated bankruptcy game are characterized by efficiency, reasonability (each claimant receives a nonnegative amount not exceeding his claim), and the thieve property. The thieve property for bankruptcy problems entails that if a claimant manages to escape with his claim, the amount allocated to each remaining claimant is not larger than his share in the original problem. Many bankruptcy rules studied in the literature are efficient, reasonable, self-consistent, and monotonic. Rules satisfying these axioms are shown to yield population monotonic allocation schemes.

Population Monotonic Allocation Schemes in Bankruptcy Games

In this paper it is shown that the core and the bargaining sets of Davis-Maschler and Zhou coincide in a class of shortest path games.

Sofia Grahn

Papers

Ideal equilibria in noncooperative multicriteria games

Cost allocation in shortest path games

Monotonic Allocation Schemes in Clan Games

Population Monotonic Allocation Schemes in Bankruptcy Games

Core and bargaining set of shortest path games