The Prisoner's Dilemma was a game constructed for a very specific purpose:
Each player has a preferred strategy that collectively results in an inferior outcome.
In game theory language, both players have a dominating strategy: regardless of the opponent's action, they should choose a specific action (in this case, an action typically called Defect). If both players choose their dominating strategy, it leads to a (Nash) equilibrium, from which no individual player benefits from deviating. This equilibrium is (Pareto) inefficient in the sense that all players prefer an alternative outcome. Let's see this in practice:
\begin{vmatrix}
\ & \color{green}{Cooperate} & \color{green}{Defect} \\
\ \color{blue}{Cooperate} & \color{blue}{4},\space\space\color{green}{4} & \color{blue}{5},\space\space\color{green}{1} \\
\ \color{blue}{Defect} & \color{blue}{1},\space\space\color{green}{5} & \color{blue}{2},\space\space\color{green}{2}
\end{vmatrix}
We see that the $\color{blue}{blue}$ player's payoff is always higher for Defect than for Cooperate; that's what it means to be a dominating strategy. The same is true for $\color{green}{green}$. If both players choose Defect, the outcome is $2,2$ which is inferior for all players to the outcome $4,4$.
Chicken was constructed in the same vein for a different purpose:
No player has a preferred strategy, and all players are in direct
rivalry with one another.
Unlike the Prisoner's Dilemma, there are no dominating strategies, and this makes a big difference. For example, what would you choose in the following game:
\begin{vmatrix}
\ & \color{green}{Cooperate} & \color{green}{Defect} \\
\ \color{blue}{Cooperate} & \space\space\space\color{blue}{0},\space\space\color{green}{0} & \space\space\space\color{blue}{2},\color{green}{-1} \\
\ \color{blue}{Defect} & \color{blue}{-1},\space\space\color{green}{2} & \color{blue}{-5},\color{green}{-5}
\end{vmatrix}
Your best strategy is to anti-coordinate with your opponent; that is, to Defect when they Cooperate and Cooperate when they Defect. But if you had a choice, you would prefer to be the one Defecting. Mutual Defection is the worst outcome and isn't an equilibrium, but neither is Mutual Cooperation. In fact, the equilibria are when you and your partner anti-coordinate and is inherently adversarial.
So in general, we have a symmetric payoff matrix:
\begin{vmatrix}
\ & \color{green}{Cooperate} & \color{green}{Defect} \\
\ \color{blue}{Cooperate} & Reward & \color{blue}{T},\space\space\color{green}{S} \\
\ \color{blue}{Defect} & \color{blue}{S},\space\space\color{green}{T} & Punish
\end{vmatrix}
- In PD, $Temptation (T) > Reward (R) > Punish (P) >
Sucker (S)$
- In Ch, $Temptation (T) > Reward (R) > Sucker (S) > Punish (P)$
While it is true that the Prisoner’s Dilemma and Chicken have a different preferential ordering of outcomes and thus different equilibria, the purposes of the two games are completely different.
Interesting Questions You Could Ask (on a Game Theory StackExchange):
- What happens when each game is iterated (i.e. multiple rounds)?
- What happens as the number of players increases (i.e public goods
game)?