Time-Varying and Scale Effect of Payoff Uncertainty on Nash Equilibrium Payoff in 2 + 2 Simulation-Based Game : A Weibull Distribution Case

We characterize the time-varying effect from payoff uncertainty where the shape parameter of Weibull distribution is changed in 2 × 2 simulation-based game. We also analyze the scale effect of strategic payoffs on the Nash equilibrium payoffs in different time-varying situations. We show that the players choose the dominant strategy but have higher expected value of the Nash equilibrium payoff with a risk premium whatever the change of time-varying effect and scale effect are. We also show that the time-varying effect from early harvest to late harvest leads to a lower average and variance of the Nash equilibrium payoff. The scale effect induces in the higher average and variance of the Nash equilibrium payoff. If players want to earn higher Nash equilibrium payoff, then they need to compare the time-varying situation with different scale effect to know the specific risk range