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Questions tagged [extensive-games]

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2
votes
2answers
41 views

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 ...
0
votes
0answers
18 views

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 ...
1
vote
1answer
45 views

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 ...
2
votes
1answer
148 views

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 ...
4
votes
2answers
65 views

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 ...
0
votes
1answer
100 views

Exercise about Monopoly price charging

In a two-period lived economy, one consumer wishes to buy a TV set in period 1. The consumer lives for two periods, and is willing to pay a maximum price of $100 per period of TV usage. In period ...
2
votes
1answer
280 views

How to demonstrate that a game always have a subgame-perfect equilibrium in pure strategies?

If I have an specific extensive game, with only a finite set of strategies, how can I demonstrate that the game always have a subgame-perfect equilibrium in pure strategies? My first intuition was to ...
6
votes
4answers
140 views

Extensive form of multiplayer games

I want to model an interaction between a government and its citizens using the game theory extensive form, but I want to express the posibility that the citizens don't act as a unique agent. For ...
1
vote
1answer
36 views

Quality Provision Game

A seller owns a single unit of an invisible good. It is worth $v(s)$ to a buyer, where $s ∈ R^+$ is the quality of the good. The function $v(·)$ is strictly increasing and strictly concave with $v(0) =...
3
votes
1answer
55 views

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 ...
2
votes
1answer
56 views

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 ...
6
votes
1answer
7k views

Difference between Sequential and Weak Sequential (Weak Perfect Bayesian) Equilibria?

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
4
votes
2answers
207 views

Proof of nestedness of subgame perfect equilibria

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 ...