My studies on the Yale web course on game theory have progressed again. The latest topics were sequential games and, as Mr. Polak put it, one of the most important concepts one might learn at Yale, backward induction.
Sequential games are games, where one player takes action first and the second one acts afterwards, knowing what the first player did. Both players also know, that the game is sequential and that the first player’s action and its results will be known to the second player before he takes action.
The key to solving sequential games is backward induction, a concept that is quite simple and very powerful. The idea of backward induction is to picture the end of the game, the last move. Whoever makes the last move, will want to maximize their payoff, as usual. When the last move is found out this way (there are potentially many options), the move before that can be solved, when considering the payoffs of the player making the second to last move: when this player knows that the player going last will maximize his payoff, he is under a constraint when maximizing his own payoff. Similarly we can work our way backwards to the beginning of the game and anticipate the first move, too. Sequential games are often modeled as decision trees.
Although backward induction is in principle easy to use. building a decision tree may be impossible due to the infinite number of possible strategies players might play. However, in such cases it may be possible to use other tools, such as calculus in optimization problems, to find out the best responses using backward induction.
In addition to backward induction, Mr. Polak also discusses moral hazard, incentives, commitment and first-mover advantage in his lectures 13 and 14. In summary the most important lessons, apart from backward induction, are:
- Moral hazard can prevent players from reaching the best possible outcome, since their incentives are not aligned, e.g. a creditor and a debtor.
- Tweaking the game and the incentives, e.g. by reducing the payoffs of some strategies, mutually better outcomes can be achieved, as incentives become aligned, e.g. a collateral for debt reduces the risk of default.
- If in a sequential game you make a public, irreversible commitment to play a certain strategy, you may force your opponent to play a certain strategy, thus securing your own payoff, e.g. a company announcing to build a new plant before their competitor and consequently increasing the market capacity to 100%, and also winning market share.
- First-mover advantage is not always prevalent, and sometimes there is a second.mover advantage, e.g. in a sequential version of rock-paper-scissors. Sometimes one might also inadvertently make oneself into the second-mover and lose the sought first-mover advantage.
For you to remember the most important of the concepts just presented, I will repeat it one more time, backward induction. Its the answer to all questions, as Mr. Polak mentions during his lecture 13.