# Three games of two-players each being played by three players simultaneously

Has the game theory literature considered situations wherein there are three two-player games being played by three players concurrently with each other; and the outcomes of those games may impact the strategies of the players in the other games. The diagram (referenced below) visualizes the situation I am describing. I have searched the literature for more than a month now but haven't seen any work on this specific topic. Has there been any work done on this topic? If you know of any such work could you please share it?

More about the two distinct games:

• Game A is a sequential game (two distinct Game A's are being played)
• Game B is played simultaneous game (like game of Chicken).

Outcomes from Game A have an impact on strategies of players in Game B and outcomes from Game B may influence the strategies of player in the two distinct Game A's.

Here is the Diagram: Three games, three players

Consider the case of $n$ players, which includes $3$ players. When pairs of players play bimatrix games (two-player strategic form games), and must play the same strategy across these games, and each player's payoff is the sum of payoffs across the all two-player games, then this is called a polymatrix game. For more info see, e.g., this tutorial:

http://event.cwi.nl/wine2015/media/slides/WINE15-Tutorial-Savani.pdf

In these games there is an interaction graph, where vertices are players and edges are bimatrix games. In your example this graph is complete (a triangle for three players), but in general it does not need to be.

More generally, games where interactions are not necessarily complete and encoded by a graph are called graphical games, see e.g.,

Michael Kearns (2007) "Graphical Games". In Vazirani, Vijay V.; Nisan, Noam; Roughgarden, Tim; Tardos, Éva (2007). Algorithmic Game Theory. Cambridge, UK: Cambridge University Press. ISBN 0-521-87282-0.

http://www.cis.upenn.edu/~mkearns/papers/agt-kearns.pdf