Write an expression for the expected utility of playing the game and for the utility associated with not playing the game. Use these expressions to determine whether you will or will not play the game one time. Suppose 100 people are endowed with the above game. Each will face an independent roll of the die. Consider a world with many agents.
Agents are alike in all respects except one.
Each agent is an expected utility maximizer. Because agents are risk averse, they are willing to buy insurance. Type G agents are low-risk agents who have a .25 probability of an accident. Type B agents are high-risk agents who have a .75 probability of an accident. The population contains equal numbers of Type G and Type B agents.