Focal point (game theory)

In game theory, a focal point (also called Schelling point) is a solution that people will tend to use in the absence of communication, because it seems natural, special, or relevant to them. The concept was introduced by the Nobel Memorial Prize-winning American economist Thomas Schelling in his book The Strategy of Conflict (1960).^[1] In this book (at p. 57), Schelling describes "focal point[s] for each person’s expectation of what the other expects him to expect to be expected to do". This type of focal point later was named after Schelling. He further explains that such points are highly useful in negotiations, because we cannot completely trust our negotiating partners' words.

Examples

Consider a simple example: two people unable to communicate with each other are each shown a panel of four squares and asked to select one; if and only if they both select the same one, they will each receive a prize. Three of the squares are blue and one is red. Assuming they each know nothing about the other player, but that they each do want to win the prize, then they will, reasonably, both choose the red square. Of course, the red square is not in a sense a better square; they could win by both choosing any square. And it is only the "right" square to select if a player can be sure that the other player has selected it; but by hypothesis neither can. However, it is the most salient and notable square, so—lacking any other one—most people will choose it, and this will in fact (often) work.

Schelling himself illustrated this concept with the following problem: "Tomorrow you have to meet a stranger in NYC. Where and when do you meet them?" This is a coordination game, where any place and time in the city could be an equilibrium solution. Schelling asked a group of students this question, and found the most common answer was "noon at (the information booth at) Grand Central Terminal". There is nothing that makes Grand Central Terminal a location with a higher payoff (you could just as easily meet someone at a bar or the public library reading room), but its tradition as a meeting place raises its salience and therefore makes it a natural "focal point".

References

↑ Schelling, Thomas C. (1960). The strategy of conflict (First ed.). Cambridge: Harvard University Press. ISBN 0-674-84031-3.

External links

Rare Entries Contests (an example) and Common Entries Contests, games of respectively avoiding and seeking out focal points
TED community experiment on focal / Schelling points

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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