Figure 2: MMPE equilibrium strategy actions with respect to utility constants. | Scientific Reports

Figure 2: MMPE equilibrium strategy actions with respect to utility constants.

From: Disease dynamics in a stochastic network game: a little empathy goes a long way in averting outbreaks

Figure 2

There are n = 4 individuals forming a star network. In cases (ac) the stage equilibrium action is unique. In case (d) there two stage equilibria. When risk averseness is weak, i.e., c0 > c1, all healthy individuals take action ai = 1 regardless of the action of the center individual. When empathy is weak, i.e., c0 > 3c2, the sick individual at the center takes action ai = 1 regardless of i’s neighbors’ actions by the same reasoning. Based on these responses we can solve for stage equilibrium in (ac). In (a) (c0 > c1 and c0 > 3c2), all individuals take action 1. In (b), because all healthy individuals take action 1 due to weak averseness, the sick individual takes action 0 considering the strong empathy (c0 < 3c2). In (c), because the sick individual takes action 1 due to weak empathy, all healthy individuals take action 0 considering their strong averseness (c0 < c1). In (d), if healthy individuals take action 1 then it is in the interest of the strongly empathetic sick individual to take action 0. However, if healthy individuals take action 0 then the sick individual receives a positive payoff from taking action 1. In both cases no individual has an incentive to deviate to another action.

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