In the game theory, a Nash equilibrium can be described as a collection of strategies, one for each player in a social game, while there is no advantage for any player to switch strategies. In such a situation, all players in the game are content with their game choices simultaneously, keeping the game at equilibrium. If you are asked to prepare an assignment based on this topic, you have come to the right place.
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While a basic introduction of the topic has been given in the beginning, let’s take a look at the Nash equilibrium definition.
Nash equilibrium is a game theory concept that determines the optimal solution in a non-cooperative game where each player lacks any incentive to change his/her initial strategy. A player does not gain anything by changing their initially chosen strategy under Nash equilibrium, given that other players also do not deviate from their initial strategy.
Nash equilibrium happens to be one of the fundamental concepts in game theory. It works on the conceptualisation of the behaviour and interactions between game participants to get the best results. It also helps predict the decisions of the players if they are making decisions at the same time, and the decision of one player takes into consideration the decisions taken by other players.
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It is important to note that there is no specific formula to calculate the Nash equilibrium. However, it can be found by modelling out different scenarios within a given game to find out the payoff of each strategy and which will be the best strategy to choose.
In the case of a two-person game, you will have to consider the possible strategies that both players can choose. If none of the players changes their strategy even after knowing all the information, then Nash equilibrium is achieved.
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The Nash Equilibrium is often compared with the dominant strategy, which happens to be another strategy of game theory. As mentioned previously, the Nash equilibrium states that the player in a game sticks to the initial strategy while knowing the opponent's strategy, and none of them changes their strategy from the initial one as long as others do not change their strategies.
Now, the dominant strategy states that the chosen strategy of the player will lead to better outcomes out of all the possible strategies that can be utilised irrespective of what strategy the opponent is using.
As you may realise, both these strategies sound a lot similar with some obvious differences. Nash equilibrium states that nothing can be gained if any of the players change their strategy when all other players maintain their strategy. According to dominant strategy, a player will choose a strategy that will produce the best outcome irrespective of what others have chosen as their strategy. Dominant strategy can be included in Nash equilibrium, while Nash equilibrium may not be the best strategy in the game.
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Nash equilibrium is quite efficient in helping a player choose the best payoff in a certain situation based not just on their decisions but also on the decisions of other players involved. Nash equilibrium can be used in different aspects of life – from developing business strategies to planning warfare.
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