Solution concepts of non- cooperative games:

While  solving a game you should keep  in  mind  that the players are  rational. They  think about their payoffs only. In  their celebrated book  "The  Theory of Games and Economic Behaviour"  John von Neumann and Oscar Morgenstern defined  a game as any  interaction between  agents that  is governed by  a set of rules specifying the possible moves for each participant  and a set of outcomes for each possible  combination  of moves. Therefore,  knowing how  to  find  a solutiori of a game  is  important  from many respects, such  as social, political and economical  aspects.  

Simultaneous games differ from sequential move games  in that players make decisions without knowing their rivals'  action. Such games are illustrated with game tables where the cells show the payoff to each player. Two person  zero sum  game,  in  which the  payoffs  sum  to  the  same  value  in  each possible outcome may be  illustrated in  shorthand with only one players payoff  in  each cell.

Nash  equilibrium  is  the  solution concept  used  to  solve simultaneous  move games. Nash equilibrium may entail pure or mixed  strategy and  can be  found using a gamut of methods. They are,  iterated elimination of strictly dominated strategies, minimax, cell-by-cell inspection. Sequential move games require players to consider the future consequences of their current move before choosing their current action. Analysis of sequential move  games generally requires the creation of  a  game tree. Backward induction  is  a method  by  which  we can find  out  the  equilibrium of  such games.

Non-credible threat  often  generates equilibria, which  are  not  realistic. Nash equilibrium fails to  bar  them  out; the concept of sub-game perfect  Nash equilibrium is useful in this regard.