What is Contest Theory?
Contest theory is a tool to describe situation where agents compete with costly efforts to win a scare prize. Quick tips: - agent: economic agent abstraction, examples include workers, sports people etc. - costly efforts: This just means the agent has to make a decision. Ie they do have infinity effort to try to win. Think of the contest people tennis players. A player cannot give 110%, it is physically impossible. - scare prize: This forces the agents to compete as they both cannot win in the contest.
Contest theory deals with various ways contests can be formulated and tried to make predictions on how rational agents would act.
Examples
As with many game theorical frameworks many situations can be appropriated. These examples are heavily influenced and borrowed from Konrad (2012) and I would recommend reading the paper. - R&D Race: When firms compete against each to win the prize of a patent we can say they are in a contest. Think of pharmaceuticals attempting to find some new cure for a disease. The first firm to discover and patent the discovery wins the prize of the government protected monopoly to sell the drug whilst the other company gets nothing for all their hard work. - Corporate Promotion Ladder: Executives in large companies are often attempting to gain a promotion. There are obviously limited higher positions available and the executives must decided how hard they wish to work to attempt to win the promotion. - Sports Contest: Sport contests are perphaps the easiest acticities to conceptually reconcile with contest theory. Think of a tennis match in the final of a grand slam. The winner gains the higher prizepool and the fame. The cost of effort include the physical pain of the match and the possibility of trying to hard leading to injury which would affect future possible earnings.
The maths
\[\begin{equation} \pi_{1} = p_{1}(e_{1}, p_{2}) * v - c(e_{1}) \end{equation}\]Here we see that the profit or utility of player 1 (in a 2 player contest) is equal to the probability of them winning (which is dictated by the contest success function) times the prize minus the cost of the players effort.
Further Reading
A must read is the novel Konrad and others (2009).
Konrad, Kai A. 2012. “Dynamic Contests and the Discouragement Effect.” Revue d’économie Politique 122 (2). Dalloz: 233–56.
Konrad, Kai A, and others. 2009. “Strategy and Dynamics in Contests.” OUP Catalogue. Oxford University Press.