Status Update: Game Theory Ahoy!

Posted on December 2, 2013

(For my last two (one, two) blog posts, I’ve been talking about prediction markets and their application to funding libre engineering and science.)

If we expect people to participate in prediction markets, fulfilling predictions to their personal financial benefit and society’s overall benefit, we have to give them some assurance that they’ll actually make money. I can’t tell people what strategy to use when buying contracts, what price to pay, when to sell, when or even how much to invest in progress on the goal itself. I could build a prediction market relatively easily, but there is little point if all I achieve is a fancy casino.

I intend to prove (or disprove, and find a new obsession) that given enough initial potential benefit distributed amongst a group of individuals, adding the ability to trade that potential benefit causes the net end-state benefit of the group to increase. If I can figure out the optimal strategy, I can answer the questions of when to buy or sell for how much and when to contribute. If outcomes are improved when players mostly use optimal strategies, I can prove prediction markets a useful mechanism.

Let’s describe the game formally:

There is one prediction under consideration. It is an open project that any player can contribute to.
The prediction has a fixed cost of completion, abbreviated P.
There are some n > 1 players. No one joins or leaves during the game.
Each player starts with some real number ≥ 0 of contracts. The total number of contracts and, equivalently, the total potential benefit is termed C_all. Player n’s number of contracts is termed C_n.
The number of contracts held by each player is public information.
Turns occur simultaneously. At each turn a player optionally expresses buy and sell offers (I’ll figure out what those look like and how they’re matched later) and optionally spends money on the project. Spending money on the project reduces P. When P is reduced to zero the game ends, otherwise another turn is played. Players’ net earnings are those earned from selling contracts plus one dollar per contract held minus what is spent buying contracts and contributing to the project.
Infinite, interestless credit is available.
There are no short positions.

I think that’s enough. If I’m successful I’ll move to progressively more realistic models.

Trivially, we can see that if C_all < P, no rearrangement of the contracts will make it rational for anyone to complete the project. If we consider only one player, it reduces to the question of whether to invest in a private good. Once we have more than one players with some contracts, things become more difficult.

I’m going to leave the analysis there for now. I’ve got a nice big book on game theory to attack. When I come back, hopefully I’ll feel better equipped to handle the task I’ve set for myself.