Following Shapley (1976), we study the problem of the existence of a Nash Equilibrium (NE) in which each trading post is either active or “legitimately” inactive, and we call it a Shapley NE. We consider an example of an exchange economy, borrowed from Cordella and Gabszewicz (1998), which satisfies the assumptions of Dubey and Shubik (1978), and we show that the trivial equilibrium, the unique...

The Aumann–Shapley [Values of Non-atomic Games, Princeton University Press, Princeton] value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault [Coherent allocation of risk capital, J. Risk 4 (1) (2001) 1]. We obtain an explicit formula for the Aumann–Shapley value, when the risk measure is given by a d...

Ginsburgh and Zang [1] consider a revenue sharing problem for the museum pass program, in which several museums jointly offer museum passes that allow visitors an unlimited access to participating museums in a certain period of time. We consider a cost sharing problem that can be regarded as the dual problem of the above revenue sharing problem. We assume that all museums are public goods and h...

Using players’ Shapley–Shubik power indices, Peleg [4] proved that voting by count and account is more egalitarian than voting by account. In this paper, we show that a stronger shift in power takes place when the voting power of players is measured by their Shapley– Shubik indices. Moreover, we prove that analogous power shifts also occur with respect to the absolute Banzhaf and the absolute J...

One basic assumption of game theory is that the players in a game can evaluate every “prospect” that might arise as an outcome of a play. Quoting Shapley (1953) “one would normally expect to be permitted to include, in the class of `prospects', the prospect of having to play a game. The possibility of evaluating a game is therefore of critical importance.” For Shapley this motivates the notion ...

In this paper we prove the existence and uniqueness of a solution concept for n-person games with fuzzy coalitions, which we call the Shapley mapping. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a “cumulative value” that is the “su...

Based on the Choquet integral and the generalized Shapley function, two new induced Atanassov’s interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov’s interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov’s interval-val...

In this paper a new model of multichoice games with a coalition structure is proposed, which can be seen as an extension of the Owen coalition structure. A coalitional value on the given model is defined, which can be seen as an extension of the Owen value. Three axiomatic systems are studied. The first one is enlightened by Owen’s characterization for the Owen value and Faigle and Kern’s chara...

This paper provides a flexible strategic framework to analyze bargaining and values in environments with coalitional externalities. Within this framework we propose a new value that extends the Shapley value to partition function form games, the so-called Rational Belief Shapley (RBS) value. We investigate the strategic foundation of the RBS value by constructing an implementation mechanism. Th...

Our input is a bipartite graph G = (R ∪ H,E) where each vertex in R ∪ H has a preference list strictly ranking its neighbors. The vertices in R (similarly, in H) are called residents (resp., hospitals): each resident seeks to be matched to a hospital while each hospital h seeks cap(h) ≥ 1 many residents to be matched to it. The Gale-Shapley algorithm computes a stable matching in G in linear ti...