# Questions tagged [extensive-games]

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### Extensive form game with multiple players

I am wondering on how to draw the extensive form with multiple players. Below is an example of the trust game. How would that look if there were two receivers with potentially different payoffs? Note ...
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### Subgame perfect Nash equilibrium when there is a tie in payoffs seems problematic

My question follows from this question: https://math.stackexchange.com/questions/2132846/game-theory-subgame-perfect-nash-equilibrium-in-a-sequential-game-with-identica from Maths stackexchange. Based ...
1 vote
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### bargaining game information/equlibria/gametree/normalform

I have a game with two players, player one offers player two one of two cars, car 1(M) has value 2 and car 2 (H) has value 1. Player two can accept (A) or reject (R) the offer. Now I have to answer ...
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### Does Subgame Perfect Nash Equilibria (SPNE) allow for credible threats?

Consider the following extensive-form game: In one alternative, Player 2 chooses G and E and Player 1 chooses D. However, Player 2 can increase her gain by making a credible threat and switch from G ...
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1 vote
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### Perfect recall vs perfect monitoring

Following my previous previous post here, I would like to add another question. Is perfect recall the same with perfect monitoring? If not, what are their differences?
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### Perfect recall assumption

When we assume that the players can recall perfectly everything about the previous stages of a game, in essence we assume that they know the history path that they followed until they reached to some ...
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### Understanding the properties of extensive form games

In Heller et al, they use the Osborne and Rubinstein formal definition for the extensive form games with public information. To some point they refer to the following two properties $P$ is a mapping ...
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### Subgame-perfect Nash equilibrium perfect information

This might be a stupid question but please bear with me. I'm trying to solve this game but I'm in doubt on how to represent the strategy profile of the game. The game looks like this in extensive-form....
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### Finding pure-strategy subgame-perfect Nash equilibria

I'm interested in finding the pure-strategy subgame-perfect Nash equilibria of the game below. What is confusing me is that after player A chooses between reducing and not reducing his end payoffs, ...
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### Could someone help guide me on finding the players with perfect recall, and those without?

Could someone help guide me on finding the players with perfect recall, and those without? For those players that do not have perfect recall, what do they forget? Step-by-step guidance would be ...
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1 vote
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### Extensive Form Representation

Question: Represent the extensive form of the game: Suppose, Nature chooses either Up or Down with probabilities 0.5 and 0.5, respectively. Then Player 1 chooses either Right or Left and does not ...
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### Obvious Dominance and Milipede Games (Question to Pycia and Troyan (2019)

I stumbled over Millipede Games and obvious Dominance in the paper "A Theory of Simplicity in Games and Mechanism Design" by Pycia and Troyan. On page 12 the authors define millipede Games. They ...
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### Extended game mixed SPNE

I have doubts about whether my solution is right. Let $x>z>y>1$. Given the extended game above, we have two subgames and will find the Nash equilibria of these. Observe that player 2 will ...
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### Confusion about multiple information Sets

I'm confronted with the following situation: First of all nature decides which of two games is played. Then each of two players make a simultaneous move, but only player I knows which game is played....
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### Sequential Game is Extensive form game?

Dynamic, Sequential, Stochastic, Extensive form and Evolutionary games. I know what all of them mean very roughly. I want to clarify them. As I understand Extensive form is a description of a ...
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### Sequential game equilibrium strategy question

The question asks for player B's equilibrium strategy, hence shouldn't player B choose the strategy that gives the highest payoff after player A's move? Why does player B choose 4 over 5 and 6 over 8 ...
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### Matchstick Game

Consider the following $2$ player finite extensive game. Player $1$ moves first. She must choose an integer from $1$ to $10$, and place that number of matchsticks on the table. Next, Player $2$ must ...
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### Strategy sets and SPNE

I need to find the startegy sets for the two players in this game. I understand that the game has only one subgame, that is, the entire game. I cannot seem to understand the strategy sets of the ...
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1 vote
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### Rigorous solution of Stackelberg leader-follower game with N-players?

In the classical two-player Stackelberg game (sequential Cournot) we have a linear demand function $P = 1 - Q$ where $Q = \sum_0^2 q_i$, and we assume homogenous production cost $c$. By starting from ...
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### Game theory - Write a maximization problem (with restriction)

I have a problem with finding a way how to solve this example: We have the company, which has two types of customers indexed as $H$ and $L$. We assume: $θ_H > θ_L$. Quantity$(Q)$ of $H$ indexed ...
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### Proper definition of extensive form game

Consider the following game: Let $N := \{1,2,3,4\}$ denote a set of agents. Going from 1 to 4 each agent can decide how many of the remaining agents he wants to integrate into a coalition. The ...
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### Extensive Form Games

( The game of “ chicken”) Two cars are driving at each other at great speeds. If nobody changes directions, in 3 seconds they will collide and die a gruesome death, yielding payoffs of −100 for both ...
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### Terminology for "part" of extensive form game

How should I call a "part" of an extensive form game which is neither (i) a subgame, nor (ii) a stage in a repeated game? For instance, consider the class of games constructed by "stacking" 2 ...
Below is a lemma which I believe to be true and which I would like to use to derive other results Take any two games in extensive form (complete information) $\Gamma$ and $\Gamma'$ differing only ...