Lewis signaling game

An extensive form representation of a two-person Lewis signalling game

In game theory, the Lewis signaling game is a type of signaling game that features perfect common interest between players. It is named for the philosopher David Lewis who was the first to discuss this game in his Ph.D. dissertation, and later book, Convention.[1]

## The game

The underlying game has two players, the sender and the receiver. The world can be in any of a number of states and the sender is aware of that state. The sender has at his disposal a fixed set of signals that he can send to the receiver. The receiver can observe the signal sent, but not the state of the world, and must take some action. For each state, there is a unique correct action and both the sender and receiver prefer that the receiver take the correct action in every state. Because both the sender and receiver prefer the same outcomes as one another, this game is a game of pure common interest.

The simplest version of this game (pictured above) has two states, two signals, and two acts.

## Equilibria

A signaling system equilibrium A pooling equilibrium A partial pooling equilibrium, dotted lines represent mixed strategies.

This game has many Nash equilibria. A few of them stand out where the sender sends a different signal in each state and the receiver takes the appropriate action in every state. Lewis dubbed these signaling systems.[1] But there are also other equilibria. In some the sender sends the same signal in every state and the receiver takes the action that is best to take given no additional information about the state of the world (pooling equilibria).

Also, when there are more than two states, signals, and acts, there are partial pooling equilibria where some information is conveyed, but some states are also pooled.[2][3]

## References

1. ↑ 1.0 1.1 Lewis, D.: 1969, Convention. A Philosophical Study, Harvard University Press, Harvard, Mass.
2. ↑ Huttegger, Simon (2007) "Evolution and Explanation of Meaning", Philosophy of Science 74(1), 1–27.
3. ↑ Pawlowitsch, Christina (2008) "Why evolution does not always lead to an optimal signaling system," Games and Economic Behavior 63: 203–226.

* v
* t
* e

Topics in game theory

Definitions|

* Cooperative game
* Determinacy
* Escalation of commitment
* Extensive-form game
* First-player and second-player win
* Game complexity
* Graphical game
* Hierarchy of beliefs
* Information set
* Normal-form game
* Preference
* Sequential game
* Simultaneous game
* Simultaneous action selection
* Solved game
* Succinct game

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
* Strategy-stealing argument
* Tit for tat
* Grim trigger
* Collusion
* Backward induction
* Forward induction
* Markov strategy

Classes
of games|

* Symmetric game
* Perfect information
* 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 game
* Strictly determined game
* Potential game

Games|

* Go
* Chess
* Infinite chess
* Checkers
* Tic-tac-toe
* Prisoner's dilemma
* Optional 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 game
* 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
* Rendezvous problem

Theorems|

* Arrow's impossibility theorem
* Aumann's agreement theorem
* Folk theorem
* Minimax theorem
* Nash's theorem
* Purification theorem
* Revelation principle
* Zermelo's theorem

Key
figures|

* Albert W. Tucker
* Amos Tversky
* Ariel Rubinstein
* Claude Shannon
* 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
* Jennifer Tour Chayes
* John Harsanyi
* John Maynard Smith
* Antoine Augustin Cournot
* John Nash
* John von Neumann
* Kenneth Arrow
* Kenneth Binmore
* Leonid Hurwicz
* Lloyd Shapley
* Melvin Dresher
* Merrill M. Flood
* Olga Bondareva
* Oskar Morgenstern
* Paul Milgrom
* Peyton Young
* Reinhard Selten
* Robert Axelrod
* Robert Aumann
* Robert B. Wilson
* Roger Myerson
* Samuel Bowles
* Suzanne Scotchmer
* Thomas Schelling
* William Vickrey

See also|

* All-pay auction
* Alpha–beta pruning
* Bertrand paradox
* Bounded rationality
* Combinatorial game theory
* Confrontation analysis
* Coopetition
* First-move advantage in chess
* Game mechanics
* Glossary of game theory
* List of game theorists
* List of games in game theory
* No-win situation
* Solving chess
* Topological game
* Tragedy of the commons
* Tyranny of small decisions

0.00

(0 votes)

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Lewis_signaling_game&oldid=285211"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template