0000000000868774
AUTHOR
Emilio Calvo
Recursive and bargaining values
Abstract We introduce two families of values for TU-games: the recursive and bargaining values. Bargaining values are obtained as the equilibrium payoffs of the symmetric non-cooperative bargaining game proposed by Hart and Mas-Colell (1996). We show that bargaining values have a recursive structure in their definition, and we call this property recursiveness. All efficient, linear, and symmetric values that satisfy recursiveness are called recursive values. We generalize the notions of potential, and balanced contributions property, to characterize the family of recursive values. Finally, we show that if a time discount factor is considered in the bargaining model, every bargaining value h…
The Serial Property and Restricted Balanced Contributions in discrete cost sharing problems
We show that the Serial Poperty and Restricted Balanced Contributions characterize the subsidy-free serial cost sharing method (Moulin (1995)) in discrete cost allocation problems.
Dynamic Models of International Environmental Agreements: A Differential Game Approach
This article provides a survey of dynamic models of international environmental agreements (IEAs). The focus is on environmental problems that are caused by a stock pollutant as are the cases of the acid rain and climate change. For this reason, the survey only reviews the literature that utilizes dynamic state-space games to analyze the formation of international agreements to control pollution. The survey considers both the cooperative approach and the noncooperative approach. In the case of the latter, the survey distinguishes between the models that assume binding agreements and those that assume the contrary. An evaluation of the state of the art is presented in the conclusions along w…
Scoring rules: A cooperative game-theoretic approach
In this work we define the game of the alternatives for each preference profile, and establish relations between scoring rules and cooperative solution concepts for that game, such as the family of semivalues and the family of least square values.
Solidarity in games with a coalition structure
Abstract A new axiomatic characterization of the two-step Shapley value Kamijo (2009) is presented based on a solidarity principle of the members of any union: when the game changes due to the addition or deletion of players outside the union, all members of the union will share the same gains/losses.
Axiomatic characterization of the weighted solidarity values
Abstract We define and characterize the class of all weighted solidarity values . Our first characterization employs the classical axioms determining the solidarity value (except symmetry ), that is, efficiency , additivity and the A-null player axiom , and two new axioms called proportionality and strong individual rationality . In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality .
A value for multichoice games
Abstract A multichoice game is a generalization of a cooperative TU game in which each player has several activity levels. We study the solution for these games proposed by Van Den Nouweland et al. (1995) [Van Den Nouweland, A., Potters, J., Tijs, S., Zarzuelo, J.M., 1995. Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research 41, 289–311]. We show that this solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995) [Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303–332]. Also, we show that the Aumann-Shapley value for continuum game…
The multichoice consistent value
We consider multichoice NTU games, i.e., cooperative NTU games in which players can participate in the game with several levels of activity. For these games, we define and characterize axiomatically the multichoice consistent value, which is a generalization of the consistent NTU value for NTU games and of the multichoice value for multichoice TU games. Moreover, we show that this value coincides with the consistent NTU value of a replicated NTU game and we provide a probabilistic interpretation.
THE SHAPLEY-SOLIDARITY VALUE FOR GAMES WITH A COALITION STRUCTURE
A value for games with a coalition structure is introduced, where the rules guiding cooperation among the members of the same coalition are different from the interaction rules among coalitions. In particular, players inside a coalition exhibit a greater degree of solidarity than they are willing to use with players outside their coalition. The Shapley value is therefore used to compute the aggregate payoffs for the coalitions, and the solidarity value to obtain the payoffs for the players inside each coalition.
Redistribution of tax resources: a cooperative game theory approach
AbstractWe consider the problem of how to distribute public expenditure among the different regions of an economic entity after all taxes have been collected. Typical examples are: the regions that make up a country, the states of a federal country, or the countries of a confederation of countries. We model the problem as a cooperative game in coalitional form, called the tax game. This game estimates the fiscal resources collected in each region, or coalition of regions, by differentiating between what comes from economic activity within each region and what comes from trade with the other regions. This methodology provides a measure of the disagreement within a region, or coalitions of re…
The equal collective gains in cooperative games
The property of equal collective gains means that each player should obtain the same benefit from the cooperation of the other players in the game. We show that this property jointly with efficiency characterize a new solution, called the equal collective gains value (ECG-value). We introduce a new class of games, the average productivity games, for which the ECG-value is an imputation. For a better understanding of the new value, we also provide four alternative characterizations of it, and a negotiation model that supports it in subgame perfect equilibrium.
Replication invariance on NTU games
Two concepts of replication (conflictual and non-conflictual) are extended from the class of pure bargaining games to the class of NTU games. The behavior of the Harsanyi, Shapley NTU, Egalitarian and Maschler-Owen solutions of the replica games is compared with that of the Nash and Egalitarian solutions in pure bargaining games.
Weighted weak semivalues
We introduce two new value solutions: weak semivalues and weighted weak semivalues. They are subfamilies of probabilistic values, and they appear by adding the axioms of balanced contributions and weighted balanced contributions respectively. We show that the effect of the introduction of these axioms is the appearance of consistency in the beliefs of players about the game.
Values of games with probabilistic graphs
Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.
A strategic approach for the discounted Shapley values
The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (Econometrica 64:357–380, 1996). We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable utility games, moreover, the model implements the \(\alpha \)-consistent values in the nontransferable utility setting.
Prices in Mixed Cost Allocation Problems
Abstract We consider mixed cost allocation problems, i.e., joint cost problems that involve two types of heterogeneous outputs, divisible and indivisible. The Aumann–Shapley price mechanism is extended to this setting. We also present a set of properties which characterize this cost sharing rule. Journal of Economic Literature Classification numbers: D63, C79.