Game Theory - Audio Ben Polak

We first play and then analyze wars of attrition; the games that afflict trench warfare, strikes, and businesses in some competitive settings. We find long and damaging fights can occur in class in these games even when the prizes are small in relation to the accumulated costs. These could be caused by irrationality or by players' having other goals like pride or reputation. But we argue that long, costly fights should be expected in these games even if everyone is rational and has standard goals. We show this first in a two-period version of the game and then in a potentially infinite version. There are equilibria in which the game ends fast without a fight, but there are also equilibria that can involve long fights. The only good news is that, the longer the fight and the higher the cost of fighting, the lower is the probability of such a fight.

We develop a simple model of bargaining, starting from an ultimatum game (one person makes the other a take it or leave it offer), and building up to alternating offer bargaining (where players can make counter-offers). On the way, we introduce discounting: a dollar tomorrow is worth less than a dollar today. We learn that, if players are equally patient, if offers can be in rapid succession, and if each side knows how much the game is worth to the other side, then the first offer is for an equal split of the pie and this offer is accepted. But this result depends on those assumptions; for example, bargaining power may depend on wealth.

We discuss auctions. We first distinguish two extremes: common values and private values. We hold a common value auction in class and discover the winner's curse, the winner tends to overpay. We discuss why this occurs and how to avoid it: you should bid as if you knew that your bid would win; that is, as if you knew your initial estimate of the common value was the highest. This leads you to bid much below your initial estimate. Then we discuss four forms of auction: first-price sealed-bid, second-price sealed-bid, open ascending, and open descending auctions. We discuss bidding strategies in each auction form for the case when values are private. Finally, we start to discuss which auction forms generate higher revenues for the seller, but a proper analysis of this will have to await the next course.

In business or personal relationships, promises and threats of good and bad behavior tomorrow may provide good incentives for good behavior today, but, to work, these promises and threats must be credible. In particular, they must come from equilibrium behavior tomorrow, and hence form part of a subgame perfect equilibrium today. We find that the grim strategy forms such an equilibrium provided that we are patient and the game has a high probability of continuing. We discuss what this means for the personal relationships of seniors in the class. Then we discuss less draconian punishments, and find there is a trade off between the severity of punishments and the required probability that relationships will endure. We apply this idea to a moral-hazard problem that arises with outsourcing, and find that the high wage premiums found in foreign sectors of emerging markets may be reduced as these relationships become more stable.

We look at two settings with asymmetric information; one side of a game knows something that the other side does not. We should always interpret attempts to communicate or signal such information taking into account the incentives of the person doing the signaling. In the first setting, information is verifiable. Here, the failure explicitly to reveal information can be informative, and hence verifiable information tends to come out even when you don't want it to. We consider examples of such information unraveling. Then we move to unverifiable information. Here, it is hard to convey such information even if you want to. Nevertheless, differentially costly signals can sometimes provide incentives for agents with different information to distinguish themselves. In particular, we consider how the education system can allow future workers to signal their abilities. We discuss some implications of this rather pessimistic view of education.

We discuss repeated games, aiming to unpack the intuition that the promise of rewards and the threat of punishment in the future of a relationship can provide incentives for good behavior today. In class, we play prisoners' dilemma twice and three times, but this fails to sustain cooperation. The problem is that, in the last stage, since there is then is future, there is no incentive to cooperate, and hence the incentives unravel from the back. We related this to the real-world problems of a lame duck leader and of maintaining incentives for those close to retirement. But it is possible to sustain good behavior in early stages of some repeated games (even if they are only played a few times) provided the stage games have two or more equilibria to be used as rewards and punishments. This may require us to play bad equilibria tomorrow. We relate this to the trade off between ex ante and ex post efficiency in the law. Finally, we play a game in which the players do not know when the game will end, and we start to consider strategies for this potentially infinitely repeated game.