Stochastic Payoff Research Articles

Cooperative games with stochastic payoffs

This paper introduces a new class of cooperative games arising from cooperative decision making problems in a stochastic environment. Various examples of decision making problems that fall within this new class of games are provided. For a class of games with stochastic payoffs where the preferences are of a specific type, a balancedness concept is introduced. A variant of Farkas' lemma is used to prove that the core of a game within this class is non-empty if and only if the game is balanced. Further, other types of preferences are discussed. In particular, the effects the preferences have on the core of these games are considered.

Stochastic cooperative games in insurance

This paper shows how problems in ‘non-life’-(re)insurance can be modeled as cooperative games with stochastic payoffs. Pareto optimal allocations of the risks faced by the insurers and the insureds are determined. It is shown that the core of the corresponding insurance games is nonempty. Moreover, it is shown that specific core allocations are obtained when the zero-utility principle is used for calculating premiums. Finally, game theory is used to give a justification for subadditive premiums.

On the instability of evolutionary stable strategies in small populations

Evolutionary stable strategies (ESSs) are often used to explain the behaviors of individuals and species. The analysis of ESSs determines which, if any, combinations of behaviors cannot be invaded by alternative strategies. Two assumptions required to generate an ESS (i.e. an infinite population and payoffs described only on the average) do not hold under natural conditions. Previous experiments have indicated that under more realistic conditions of finite populations and stochastic payoffs, populations may evolve in trajectories that are unrelated to an ESS, even in very simple evolutionary games. The simulations are extended here to small populations with varying levels of selection pressure and mixing levels. The results suggest that ESSs may not provide a good explanation of the behavior of small populations even at relatively low levels of selection pressure and even under persistent mixing. The implications of these results are discussed briefly in light of previous literature which claimed that ESSs generated suitable explanations of real-world data.

On the instability of evolutionary stable strategies

Evolutionary stable strategies (ESSs) are often used to explain the behaviors of individuals and species. The analysis of ESSs determines which, if any, combinations of behaviors cannot be invaded by alternative strategies. However, two of the assumptions required to generate ESSs, an infinite population and payoffs described only on the average, are not particularly realistic in natural situations. Previous experiments have indicated that under more natural conditions of finite populations and stochastic payoffs, populations may evolve in trajectories that are unrelated to an ESS, even in very simple evolutionary games. Those earlier simulations are extended here under a variety of conditions. The results suggest that ESSs may not provide a good explanation of a finite population's behavior even when the conditions correspond closely with the infinite population model. The implications of these results are discussed briefly in light of previous literature claiming that ESSs generated suitable explanations of real-world data.

Cooperative Games with Stochastic Payoffs: Deterministic Equivalents

This paper focuses on the subclass of cooperative games with stochastic payoffs in which the preferences of the agents are such that a stochastic payoff can be represented by a deterministic equivalent. To each game within this class one can associate a game with deterministic payoffs. It is shown that the core of such a cooperative game with stochastic payoffs is nonempty if and only if the core of the associated game is nonempty.

Stochastic Cooperative Games in Insurance and Reinsurance

This paper shows how problems in non life-insurance and non life-reinsurance can be modelled simultaneously as cooperative games with stochastic payoffs. Pareto optimal allocations of the risks faced by the insurers and the insureds are determined. It is shown that the core of the corresponding insurance games is nonempty. Moreover, it is shown that specific core allocations are obtained when the zero utility principle is used for calculating premiums. Finally, game theory is used to give a justification for subadditive premiums.

Letter to the Editor—Choosing Among Investment Possibilities with Stochastic Pay-Off Minus Expenditure

A multiperiod investment problem with stochastic pay-off minus expenditure is described. This problem can be solved by the method for solving discrete optimization problems of Lawler and Bell.