Secondly ever finite game with perfect information can be solved using backward inductions which gives the result.
Suppose that two firms 1 and 2 produce an identical good ie consumers do not care who makes the good. All of the good is sold but the price depends on the number of goods:. However we will modify this to assume that there is a leader and a follower, ie the firms do not decide at the same time.
This game is called a Stackelberg leader follower game. We use backward induction to identify the Nash equilibria. Improve this answer. Arthur Tarasov Arthur Tarasov 1, 10 10 silver badges 16 16 bronze badges. Moves are components of players' strategies in sequential games. In fact, I could probably replace words 'moves' with 'strategies', but I think it would be a little less accurate and not less confusing.
In my opinion the idea of converting extensive form sequential games into normal form is itself confusing and something mathematicians would have fun with. I can't think of any practical use for it. It seems to be some mix of action and decision point. Of course you are free to clarify your answer, but why in this comment, why not in the answer itself? I think move is the same as action. We can then say that a strategy is a complete set of actions.
When these actions are in sequence, they can be referred to as moves. Much like they call actions moves in any sequential sports game like chess. Show 5 more comments. Community Bot 1. It reminds me of the guess and verify solutions I sometimes see in differential games.
Sign up or log in Sign up using Google. Consider the following game: a. Find the pure-strategy Nash equilibria if any. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions.
Compute players' expected payoffs in the equilibria found in parts a and b. Draw the extensive form for this game. The mixed-strategy Nash equilibrium in the Battle of the Sexes in Table 8. The game of Chicken is played by two macho teens who speed toward each other on a single-lane road.
The first to veer off is branded the chicken, whereas the one who doesn't veer gains peer-group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the Chicken game are provided in the following table. Draw the extensive form. Find the pure-strategy Nash equilibrium or equilibria. Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best-response function diagram for the mixed strategies.
Write down the normal and extensive forms for the sequential version of the game. Maths Maths 1. Add a comment. Active Oldest Votes. Improve this answer. Regio Regio 4, 1 1 gold badge 3 3 silver badges 16 16 bronze badges. Thanks for pointing it out. So he has to choose between U 1 or D 0. Clearly he chooses U. Hope that helps! Lee Sin Lee Sin 3 3 silver badges 13 13 bronze badges. Featured on Meta. New post summary designs on greatest hits now, everywhere else eventually.
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