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November 07, 2004

Unifying Ideas in Game Theory: Symmetric-Player Games vs. Principal-Agent Games

I'm trying to work on a 4th edition of http://www.rasmusen.org/GI/index.html, and thinking about big ideas.

There is one large class of games in which one player moves first to try to get another to do something-- the principal-agent games, broadly construed. These include games of boss and worker, voter and politician, customer and seller. The player in this first class of games are in asymmetric positions-- they choose different sorts of actions. In some of these games-- the "moral hazard" ones-- the problem is that the agent's action is unobserved. In others-- the "adverse selection" games-- the problem is that the agent has some information the principal does not know.

In a second large class of games-- shall I call them "symmetric player games"?-- the players are all in the same sort of position-- two countries at war, or five firms setting prices, or two politicians choosing campaign spending. The idea of strategic substitutes and complements applies to these games, and is a unifying idea I'd like to use more. The idea is that in some games, when the other player does more of his strategy, I want to do more of mine. If my competitor raises his price, I want to raise mine. If my rival for elected office spends more on advertising in Wisconsin, I want to spend more too. We call this a situation of "strategic complements". In other situations, when my rival does more of his strategy, I do *less* of mine. If the rival firm increases capacity, I reduce my capacity. If the other firm spends more on research, I give up on research altogether. This is a situation of "strategic substitutes"....

... I realize that my chapters on Bargaining and Auctions can be roughly differentiated in this way. The usual bargaining game is one of strategic substitutes. If my rival is tougher, I will be softer, lest the bargain fall through. The usual auction game is one of strategic complements. If my rival bids higher, I will bid higher too. This is true even though the auction game is a mixed principal-agent/symmetric-player game, the principal being the seller and the agents being the bidders.

This makes me wonder where I should put my Pricing chapter. Already, I've decided to carve up the Entry chapter and move its pieces to other chapters or delete them. Pricing is the lone remaining application-centered chapter. Maybe it should be carved up too.

Another dichotomy is between games in which players take the rules as given, and "mechanism design" games, or "contracting games", in which they start by trying to bind themselves to the rules that will incentivize their behavior later in the game. I am not sure how to incorporate that dichotomy. Contracting games obviously arise most in principal-agent games, with the boss designing a contract for a worker (which, usually but not always, must satisfy a "participation constraint" that the worker be willing to accept it instead of quitting the job), or voters designing a constitution for politicians. In other principal-agent games, however, there is no contracting. Signalling games are the most prominent of these: workers choose credentials to signal their ability, without any formal contract offer beforehand by firms.

But contracting arises in symmetric player games too. Classic mechanism design problems include a seller setting the rules for an auction for lots of symmetric bidders, or a boss setting the rules for promotion for workers in a tournament with each other. Those two examples are mixed principal-agent/symmetric-player games, but mechanism design can even arise in pure symmetric-player games: a cartel chooses rules for punishing members who cut prices, a team of workers agrees to a sharing rule for output, or a group of citizens agrees to a choice rule for choosing how much each person pays for a new streetlight and whether it is built based based on announced preferences.

Posted by erasmuse at November 7, 2004 03:11 AM

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