Write down this game in extensive form (HINT: this game is commonly called the centipede game because its game tree resembles a centipede). How many information sets does each player have? How many strategies does each player have?

Explanation:

In game theory, the game of centipede (or centipede), first introduced by Rosenthal in 1981, is an extended form game in which two players take turns choosing between taking a payoff, which grows as it does not you choose to acquire it, and thus end the game, or pass the choice to another player.

The payoffs are however arranged in such a way that if one passes the choice to the opponent and the opponent chooses the payoff in his turn, the player who had passed receives a slightly lower payoff than he would have taken if he had finished the game in his round.

The only perfect Nash balance in the subgames (and every Nash balance) of this game indicates that player 1 should take the payoff in the first game round and leave player 2 with his mouth dry; however, by testing the game empirically, few players do, and as a result they get a higher payoff than expected in the balance analysis.

These results show how a game's solutions represented by the perfect Nash equilibrium in subgames and the Nash equilibrium cannot predict how people play in some circumstances.

The game of centipede is commonly used in introductory courses in game theory to highlight the concept of backward induction and the iterated elimination of dominated strategies, which constitute