Questions tagged [dynamic-games]

Questions related to the application of game theory to situations in which actions are taken sequentially.

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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 ...
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Solved examples of Nash equilibria in dynamic games in discrete-time

I am reading the Handbook of Dynamic Game Theory by Bassar and Zaccour. In the first chapter, titled Multistage Games, they discuss dynamic games in discrete time specified as follows: A set of ...
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Markov Perfect Nash Equilibrium: what do the players need to know?

I am studying dynamic games and I would like some clarifications on the notion of Markov Perfect Nash Equilibrium. Before illustrating my doubt, let me describe the basic framework. Consider a game ...
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2 votes
1 answer
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Relation between Markov Perfect Nash Equilibrium and Markovian evolution of the state

I am studying dynamic games and I'm fundamentally confused about the relation between Markov Perfect Nash Equilibrium and Markovian evolution of the state. Before illustrating my doubt, let me ...
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1 vote
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Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?

I read some lectures on the Spence's model. Some (see e.g. P31 of lecture PPT from MIT game thoery course) mention that SE imposes no restrictions on the off-equilibrium beliefs but without proof. I ...
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3 votes
1 answer
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Design of efficient cheap talk communication

Are there any papers about efficient cheap talk communication, where the players achieve the equilibrium payoffs of a correlated strategy as in Aumann's seminal paper? Or in case no such paper exists, ...
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4 votes
1 answer
59 views

Correlation device that induces a specific transition probability

Taking a look at this paper of Forges and Vida the authors define a correlation device in page $102$, that is a standard probability space $\left(\Omega,\mathcal{B},\mu\right)$, They assume that the ...
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2 votes
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48 views

Repeated Games of Incomplete information set up and questions

The following are from the model of Jérôme Renault (Repeated Games of incomplete infomration). The preliminaries of the model Formally, a repeated game with incomplete information is given by the ...
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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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Definition of the space of a repeated game

I want to define the space of a stochastic game and it confuses me a lot, so I want someone to check please the space $\Theta$ that I define at the end and how could I define the sigma algebra of this ...
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How to define a dynamic programming problem in an incomplete information game?

How can I define a problem of dynamic programming, to use the Hamilton-Jacobi-Bellman equation in order to solve the utility maximization problem of the generic agent of a dynamic game with incomplete ...
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Strange screening game were FS contracts equals optimal contracts

Consider the setting where a principal hires an agent to do a project. Payoff from project is $\pi = \beta e$, where $\beta \in \{1,2\}$ is the degree of the agent's talent and $e \in [0, +\infty]$ is ...
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1 vote
1 answer
244 views

Simultaneous vs Sequential Games [closed]

Is there a way to characterize the distinction between simultaneous vs sequential games? I'm trying to describe a situation where players can only take actions without knowledge of other players' ...
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4 votes
1 answer
137 views

Finitely repeated Prisoner’s Dilemma with switching cost

I'm doing this finitely repeated Prisoner's dilemma with switching costs but I have trouble showing the fact that $\varepsilon$ had to be $1 < \varepsilon < 2$. I do see why and that it is a ...
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2 votes
0 answers
81 views

Fehr-Schmidt, Ultimatum game, Subgame-Perfect Nash Equilibrium

I'm studying the different variations of the ultimatum games. I've spent some time on this following game: Assume now that each player does not only care about the amount of money she receives, but ...
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2 votes
2 answers
276 views

Pure-Strategy Bayesian Nash equilibrium with general common prior

I'm doing a problem set on the subject of Bayesian Nash equilibrium. I'm asked to find the pure-strategy BNE of the following. I've calculated to matrix shown below. My first concern is if I've ...
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2 votes
1 answer
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Estimation of point-identified Dynamic Discrete Choice models with moment inequalities

I'm trying to understand and implement in code the method in Bajari, Benkard, Levin (2007). The first stage is clear to me, as well as how to forward-simulate to obtain an estimate of the value ...
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2 votes
4 answers
124 views

How to achieve the best outcome by a single statement in this game?

This game is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which contenders practice brinksmanship to their own advantages. It goes as follows: Anderson, Barnes, and ...
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1 answer
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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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2 votes
1 answer
119 views

Definition of subgame perfect Nash equilibrium

Take a two-stage game with complete information and simultaneous actions in each state: (1) Player 1 and 2 simultaneously choose action $a_1\in A_1$ and $a_2\in A_2$ respectively. (2) Player 1 and ...
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5 votes
1 answer
238 views

What is the game theory of retaliatory trade tariffs?

Suppose no tariffs, or negligible tariffs, exist between nations A and B, and suddenly A introduces substantive tariffs on certain products A imports from B. In theory, this could lead to B and A ...
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0 votes
1 answer
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Spence's Job Market Signaling Game

I have a little doubt in the Job Market Signalling Game. I am referring to A Primer in Game Theory: Gibbons, Chapter 4, Signaling Games The attached paragraph refers to a Separating Equilibrium case ...
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2 votes
1 answer
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Repeated Game SPNE

I approached this question in this way: $(P_1,P_2), (R_1,R_2), (S_1,S_2)$ are the Nash Equilibria of the Stage 1 game. For the given strategy to be sustained as SPNE, there should be no way unilateral ...
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1 vote
1 answer
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SPNE and Pareto Optimality

"The SPNE of a sequential game might not necessarily be Pareto Optimal" I understand the definitons of Nash Equilibria and Pareto Optimality and that these are not synonymous concepts. An example in ...
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-1 votes
1 answer
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Sequential Bertrand game with differentiated goods, how to write the strategies of firm 2 [closed]

In a Bertrand competition with differentiated goods where firms set the prices sequentially, we have the following demand functions: q1 is quantity of goods demanded for firm 1 q2 is quantity of ...
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2 votes
0 answers
224 views

Subgame Perfect Equilibrium with Pure Strategies in Sequential Games [closed]

If I have a sequential game, i.e. in each node (that I will call $t$) only one player choose an strategy from a finite space of strategies, Is it true there always exist a subgame perfect equilibrium ...
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2 votes
2 answers
135 views

Price setting firms with cost reduction technology

As part of my undergraduate studies in Industrial Economics, I am trying to solve the following question: Two price-setting firms are competing in a market for a homogeneous product. There are 10,...
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3 votes
1 answer
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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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1 vote
1 answer
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World as a society of interlinked multiplayer individuals

If you were to take a game-theoretic model of a world in which each individual tried to optimize their utility function / goals then how would you go about designing a computer simulation of the ...
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1 vote
0 answers
85 views

Dynamic dividing a dollar game

The question is a reformulation of an incomplete version. Consider the following dynamic dividing a dollar game where agent 1 claims $x(t)$ of the dollar and agent 2 $y(t)$ (paper). \begin{align} &...
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1 vote
0 answers
67 views

Dynamic contract theory: Demarzo, Fishman(2007) optimal long term financial contracting

I am reading Demarzo, Fishman(RFS,2007). Any suggestion will be appreciated. My questions are the following: (a) \begin{equation*} b_T^e(a) = \left\{\begin{array}{lll} -e^{(\gamma-r)(...
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2 votes
1 answer
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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 ...
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6 votes
2 answers
211 views

Multiple equilibria: which one to select?

There are two agents $i=1,2$. Consider the following programm \begin{align} &V_1(x_0) := \max_u \int^\infty_0 e^{-\rho t}F_1(x(t),u(t),v(t))dt\\ &V_2(x_0) := \max_v \int^\infty_0 e^{-\rho t}...
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3 votes
0 answers
67 views

Converging Trajectories and Sufficiency for Optimality

(The question is loosely relatet to this thread.) In the paper "Feedback Equilibria for a class of non-linear Differential Games" by Mäler et al. it is stated (p. 14) In fact sufficiency is ...
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5 votes
0 answers
103 views

Can repeated bidding in an auction make each player's type common knowledge?

In Benjamin Edelman, Michael Ostrovsky, and Michael Schwarz(2007), there's a hand-waving argument to justify their setting as a game of complete information: we assume that all values are common ...
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7 votes
1 answer
119 views

How to verify Value Function in nonzero sum two player Differential Game?

There are two agents $i=1,2$. The state $k$ is governed by $\tau_i\in[0,1]$ where \begin{align} \dot{k} = f(k,\tau_1,\tau_2). \end{align} Define the value function of player $i$ by \begin{align} v_i(...
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9 votes
1 answer
353 views

What does Battigalli really mean by "Players can not choose strategies, they can only choose actions."?

In this video (from 7: 30 to 9: 00)on Youtube, Battigalli mentions the state of world for a simple three-legged centipede game, which, in his own word, is "$\ldots$a description of everything ...
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5 votes
2 answers
143 views

Repeated games without a beginning and an end

I'm interested to know results on repeated games indexing each stage game by $\mathbb Z$ which contrast with those indexed by $\mathbb Z_+$. It seems to me this could be quite different from repeated ...
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7 votes
1 answer
253 views

Models for online markets with reputation system

The only relevant model I'm aware of is Liu Qingmin(2011 R.E.S). Is there any other decent models dealing with the mechanism of online markets under reputation system, and perhaps linking to ...
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5 votes
2 answers
630 views

One-shot deviation principle for infinite repeated games and dynamic programming

In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming. Because, in repeated games, a one-shot ...
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8 votes
1 answer
330 views

Identification with BBL

In the last few years, the estimator proposed by Bajari, Benkard, and Levin ('07) for dynamic games has been gaining popularity. It is relatively straight forward and is one of the only viable options ...
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