Enumerative combinatorics
A value for games with n players and r alternatives
International Journal of Game Theory
International Journal of Game Theory
A consistent value for games with n players and r alternatives
International Journal of Game Theory
The Shapley-Shubik power index for games with several levels of approval in the input and output
Decision Support Systems - Special issue: Decision theory and game theory in agent design
The Banzhaf power index for ternary bicooperative games
Discrete Applied Mathematics
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The present paper introduces bicooperative games and develops some general values on the vector space of these games. First, we define biprobabilistic values for bicooperative games and observe in detail the axioms that characterize such values. Following the work of Weber [R.J. Weber, Probabilistic values for games, in: A.E. Roth (Ed.), The Shapley Value: Essays in Honor of Lloyd S. Shapley Cambridge University Press, Cambridge, 1988, pp. 101-119], these axioms are sequentially introduced observing the repercussions they have on the value expression. Moreover, compatible-order values are introduced and there is shown the relationship between these values and efficient values such that their components are biprobabilistic values.