377 research outputs found
Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games
Cooperative games provide a framework for fair and stable profit allocation
in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are
such solution concepts that characterize stability of cooperation. In this
paper, we study the algorithmic issues on the least-core and nucleolus of
threshold cardinality matching games (TCMG). A TCMG is defined on a graph
and a threshold , in which the player set is and the profit of
a coalition is 1 if the size of a maximum matching in
meets or exceeds , and 0 otherwise. We first show that for a TCMG, the
problems of computing least-core value, finding and verifying least-core payoff
are all polynomial time solvable. We also provide a general characterization of
the least core for a large class of TCMG. Next, based on Gallai-Edmonds
Decomposition in matching theory, we give a concise formulation of the
nucleolus for a typical case of TCMG which the threshold equals . When
the threshold is relevant to the input size, we prove that the nucleolus
can be obtained in polynomial time in bipartite graphs and graphs with a
perfect matching
The Least-core and Nucleolus of Path Cooperative Games
Cooperative games provide an appropriate framework for fair and stable profit
distribution in multiagent systems. In this paper, we study the algorithmic
issues on path cooperative games that arise from the situations where some
commodity flows through a network. In these games, a coalition of edges or
vertices is successful if it enables a path from the source to the sink in the
network, and lose otherwise. Based on dual theory of linear programming and the
relationship with flow games, we provide the characterizations on the CS-core,
least-core and nucleolus of path cooperative games. Furthermore, we show that
the least-core and nucleolus are polynomially solvable for path cooperative
games defined on both directed and undirected network
Investment under ambiguity with the best and worst in mind
Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical
Under stochastic dominance Choquet-expected utility and anticipated utility are identical
The aim of this paper is to convince the reader that Choquet-expected utility, as initiated by Schmeidler (1982, 1989) for decision making under uncertainty, when formulated for decision making under risk naturally leads to anticipated utility, as initiated by Quiggin/Yaari. Thus the two generalizations of expected utility in fact are one
Information and ambiguity: herd and contrarian behaviour in financial markets
“The final publication is available at Springer via http://dx.doi.org/10.1007/s11238-012-9334-3”The paper studies the impact of informational ambiguity on behalf of informed traders
on history-dependent price behaviour in a model of sequential trading in nancial markets.
Following Chateauneuf, Eichberger and Grant (2006), we use neo-additive capacities to
model ambiguity. Such ambiguity and attitudes to it can engender herd and contrarian
behaviour, and also cause the market to break down. The latter, herd and contrarian
behaviour, can be reduced by the existence of a bid-ask spread.Research in part funded by ESRC grant RES-000-22-0650
Differential information in large games with strategic complementarities
We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required
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