Types of Game Theory

Cooperative Game :

 It is an economic game played by firms in which players or firms can negotiate on binding contracts which allows them  to make mixed or joint strategies.

Example: Ahmed and Ali are buyer and seller respectively and they are bargaining over the price of a smartphone.  If the smartphone’s cost of production is  Rs.10,000 and Ahmed values the smartphone at Rs 15,000, then a cooperative solution to  this game is possible. Now an agreement to sell smartphone at any price between Rs 10,001- Rs14,999  will maximize Ahmed`s  consumer surplus and Ali`s profit  and both buyer and seller will be  made better off.

In above paragraph it was the example of Ali and Ahmed where we learnt how they both were made better off through cooperative game.  Now if two firms involve in a joint investment to develop a new application for a smartphone and if they can sign a binding contract to divide the profit from their joint investment then a cooperative outcome is possible because it will make both the firms better off.

Non Cooperative Game

A non cooperative game is a game in which negotiating  and enforcement of binding contracts are not possible.

Example:  Suppose Ali , who is at an auction of cars , he is a bidder and he wants to buy himself a car. Ali`s strategy is to bid first and bid an amount of $10,000 and he wants to make an early impression or convince other competitive buyers that he is a serious buyer and he really wants to buy that specific car but at the same time Ali also has decided  that he will stop bidding if other bidders bid over $50,000. In  this example , Ali and every other bidder will take each others actions or behaviors or decisions quite seriously and take that into account for consideration while deciding an optimal bidding strategy for their payoff.

The basic fundamental difference between cooperative and a non cooperative game lies in the possibilities of contracts. Binding contracts are possible in cooperative games  and binding contracts are not possible in non cooperative games. For both the games it is very necessary to understand your opponent`s point of view and reduce his likely response to your actions.

Some other games are as follows:

Repeated Game :

                   A type of game in which actions are taken and payoffs are received over and over again.

Sequential Game

                               A type of  game in which players respond to each others actions and reactions.

Strategies  in Game Theory

1. Dominant strategies
2. Pure Strategies
3. Mixed Strategies

1. Dominant Strategies:

                                 Dominant strategy is a strategy which is optimal regardless of what other players do. It means you perform an action without caring about your competitor`s action or you simply don`t care about what other players do , you are only concerned with maximizing your own payoff. Let`s look at an example:

In the above example both Ali and Ahmed can charge low or high prices. The above numbers in the cells of matrix tells us about the actions of both sellers and also the payoffs  that they both  would receive. If both Ali and Ahmed charge high price for their products then both willl get a payoff of (15,15) and if they both charge low prices then each of them will receive payoff of (10,10). Now if Ahmed charge high price and Ali charges low price , then Ali  will make  higher profit of 20 and Ahmed will make low profit of 5 only. On the other hand, if Ali charges high price and Ahmed charge low price then Ahmed will make a higher profit of 20 and Ali will make only 5. It means that , If Ahmed charge high price and Ali charge low price then profit of 20 is better than 15 for Ali. Now if Ahmed charge low price, then 10 is a better profit than 5. So, Ali will again charge low price. Now this means  Ali has a dominant strategy which is charging a low price. Same is the case for Ahmed and for him the Dominant strategy  is also to charge low price. Now the equilibrium outcome will be (10,10) and it will be the profit that Ali and Ahmed will make and it will be the profit made by these two regardless of what each of them do.

The Nash Equilibrium

                          Nash equilibrium is a set of actions or strategies.  Actions taken by each player, who is doing the best he can , given the actions of their opponents. It means the strategies of each player is stable and they are satisfied with their best possible decision and they will not change it. Nash equilibrium is also a Cournot equilibrium because in Cournot equilibrium every producers sets its own output , while taking the outputs of other competitive producers fixed and has no incentive  to change the level of its output because each producer is doing the best , given the other competitor`s  decision.

Example :                                                                                   The Battle of Sexes

In the above matrix numbers show payoffs and actions . Anjelina and Watson are husband and wife and they are a lovely couple. Anjelina and Watson  are here the two players of the game and their actions are watching T.V Show or T20 cricket match respectively. Watson wants to watch his favourite team “Sydney Sixer`s T20 match Vs Hobart Hurricanes” but at same time he wants to be with Anjelina as well so, the resulting payoff for Watson is (5,4). On the other hand Anjelina wants to watch her favourite T.V Show ” Grey`s Anatomy ” and she also wants to be with Watson while watching T.V Show  and her payoff that she would receive will be (4,5). Now If they both end up and they watch seperately , then the payoff they both would receive will be (0,0). Which means that they will watch what they want  to but they won`t be together while watching. If both of them watch T20 cricket match between “Sydney Sixers and Hobart Hurricanes”  the payoff they would receive will be (5,4) and If the both watch “Grey`s Anatomy” the payoff would be (4,5). Now they will not watch seperately in order to avoid (0,0)  outcome or payoff.  So ,how this will solve the case for us ?. The answer is as Nash equilibrium is set of actions or strategies  so, Dominant strategy  will solve this case. Suppose if Anjelina was to watch the T20 Match between Sydney Sixers and Hobart Hurricanes and same Watson wanted to watch  and If Anjelina were to watch T.V show “Grey`s Anatomy” then Watson will also watch T.V show. On the other side , If Watson wanted to watch T20 Match  then Anjelina  will also watch T20  match . So, the resulting payoff will  be both Watson and Anjelina watching T20 match  together will turn out to be a Nash Equilibrium. Nash equilibrium concept tells us about a situation where both players do their best and where they are happy but in Battle of Sexes case one can say that watching T.V is also a nash. In Battle of Sexes more than one nash equilibrium exists.

Pure Strategy :

A player of a game or a firm  who takes a specific action to maximize his payoff or makes specific strategy to increase their payoff.

Mixed Strategy :

Mixed Strategy is a one in which a player makes random choice between  two or more possible actions that can be taken but those actions taken are based on a set of chosen probabilities. The basic difference between pure strategy and mixed strategy is that in pure strategy people makes specific actions but  in mixed strategy actions are taken randomly or actions are based on probabilities.