Simultaneous game
In other words, both players normally act at the same time in a simultaneous game.
In sequential games, players observe what rivals have done in the past and there is a specific order of play.
[5] A simple example is rock-paper-scissors in which all players make their choice at exactly the same time.
The key to modeling simultaneous games in the extensive form is to get the information sets right.
An example of a simultaneous 2-player game: A town has two companies, A and B, who currently make $8,000,000 each and need to determine whether they should advertise.
A zero-sum game is when the sum of payoffs equals zero for any outcome i.e. the losers pay for the winners gains.
An example of a simultaneous 3-player game: A classroom vote is held as to whether or not they should have an increased amount of free time.
In simultaneous games, the best move a player can make is to follow their dominant strategy, if one exists.
[11] When analyzing a simultaneous game: Firstly, identify any dominant strategies for all players.
[11] Some people always expect the worst and believe that others want to bring them down when in fact others want to maximise their payoffs.
[10] A pure Nash Equilibrium is when no one can gain a higher payoff by deviating from their move, provided others stick with their original choices.
The game is usually presented as follows: Two members of a criminal gang have been apprehended by the police.
Therefore, betrayal provides a greater reward for a majority of the potential outcomes.
The choice to cooperate clearly provides a better outcome for the two prisoners however from a perspective of self interest this option would be deemed irrational.
Simultaneous games are designed to inform strategic choices in competitive and non cooperative environments.
However, is important to note that Nash equilibria and many of the aforementioned strategies generally fail to result in socially desirable outcomes.
Pareto efficiency is a notion rooted in the theoretical construct of perfect competition.
Originating with Italian economist Vilfredo Pareto the concept refers to a state in which an economy has maximized efficiency in terms of resource allocation.
[13] The Stag Hunt by philosopher Jean-Jacques Rousseau is a simultaneous game in which there are two players.
Thus, providing the potential for a player to receive no payoff should they be the only party to choose to hunt a Stag.
The game is designed to illustrate a clear Pareto optimality where both players cooperate to hunt a Stag.
It is imperative to note that Pareto optimality is not a strategic solution for simultaneous games.
Moreover, potentially providing insight into how players should learn to play over time.
