2

3. Betting Gain-3*. There are three states of the world: {ashram erg}. Each player has two actions available: to bet (B) or not to bet (:1. Betting costs 1 euro whatever the choice of the other player. If the two players decide to bet and the realized state of the world is all, then Player 2 gives 2 euros to Player 1. If the two players players decide to bet and the realized state is ragj then Player 1 gives 3 euros to Player 2. If the two players decide to bet and the state realized is cog, then Player 2 gives 5 euros to Player 1. The a priori probability distribution is Maul) = phag) = Mug). Player 1 only knows if the state is an or not. Player 2 only knows if the state is M3 or not. (a) Represent the Bayesian game under normal form 2 write down the 3 payoff matrices {one for each state) (b) Show that this equilibrium has a unique (Bayesian) Nash equilibrium