In game theory, a cursed equilibrium is a solution concept for static games of incomplete information. It is a generalization of the usual Bayesian Nash equilibrium, allowing for players to underestimate the connection between other players' equilibrium actions and their types – that is, the behavioral bias of neglecting the link between what others know and what others do. Intuitively, in a cursed equilibrium players "average away" the information regarding other players' types' mixed strategies.

The solution concept was first introduced by Erik Eyster and Matthew Rabin in 2005, and has since become a canonical behavioral solution concept for Bayesian games in behavioral economics.

Let ${\displaystyle I}$ be a finite set of players and for each ${\displaystyle i\in I}$, define ${\displaystyle A_{i}}$ their finite set of possible actions and ${\displaystyle T_{i}}$ as their finite set of possible types; the sets ${\displaystyle A=\prod _{i\in I}A_{i}}$ and ${\displaystyle T=\prod _{i\in I}T_{i}}$ are the sets of joint action and type profiles, respectively. Each player has a utility function ${\displaystyle u_{i}:A\times T\rightarrow \mathbb {R} }$, and types are distributed according to a joint probability distribution ${\displaystyle p\in \Delta T}$. A finite Bayesian game consists of the data ${\displaystyle G=((A_{i},T_{i},u_{i})_{i\in I},p)}$.

For each player ${\displaystyle i\in I}$, a mixed strategy ${\displaystyle \sigma _{i}:T_{i}\rightarrow \Delta A_{i}}$ specifies the probability ${\displaystyle \sigma _{i}(a_{i}|t_{i})}$ of player ${\displaystyle i}$ playing action ${\displaystyle a_{i}\in A_{i}}$ when their type is ${\displaystyle t_{i}\in T_{i}}$.

For notational convenience, we also define the projections ${\displaystyle A_{-i}=\prod _{j\neq i}A_{j}}$ and ${\displaystyle T_{-i}=\prod _{j\neq i}T_{j}}$, and let ${\displaystyle \sigma _{-i}:T_{-i}\rightarrow \prod _{j\neq i}\Delta A_{j}}$ be the joint mixed strategy of players ${\displaystyle j\neq i}$, where ${\displaystyle \sigma _{-i}(a_{-i}|t_{-i})}$ gives the probability that players ${\displaystyle j\neq i}$ play action profile ${\displaystyle a_{-i}}$ when they are of type ${\displaystyle t_{-i}}$.

Definition: a Bayesian Nash equilibrium (BNE) for a finite Bayesian game ${\displaystyle G=((A_{i},T_{i},u_{i})_{i\in I},p)}$ consists of a strategy profile ${\displaystyle \sigma =(\sigma _{i})_{i\in I}}$ such that, for every ${\displaystyle i\in I}$, every ${\displaystyle t_{i}\in T_{i}}$, and every action ${\displaystyle a_{i}^{*}}$ played with positive probability ${\displaystyle \sigma _{i}(a_{i}^{*}|t_{i})>0}$, we have

where ${\displaystyle p_{i}(t_{-i}|t_{i})={\frac {p(t_{i},t_{-i})}{\sum _{t_{-i}\in T_{-i}}p(t_{i}|t_{-i})p(t_{-i})}}}$ is player ${\displaystyle i}$'s beliefs about other players types ${\displaystyle t_{-i}}$ given his own type ${\displaystyle t_{i}}$.

First, we define the "average strategy of other players", averaged over their types. Formally, for each ${\displaystyle i\in I}$ and each ${\displaystyle t_{i}\in T_{i}}$, we define ${\displaystyle {\overline {\sigma }}_{-i}:T_{i}\rightarrow \prod _{j\neq i}\Delta A_{j}}$ by putting