# Questions tagged [dynamic-games]

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

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22 views

### Finding strategies and subgame perfect equilibria

In my game theory class we recently learned about dynamic games and I wanted to know whether I solved my homework problem correctly (and how to attempt the second part). a) Determine all strategies ...
12 views

### Dynamic price competition with capacity constraints

I have a dynamic price (Bertrand) competition with 2 players with the same capacity constraints. Grim trigger strategy is to set monopoly price at t=0 or if the monopoly price was set by both players ...
1 vote
105 views

### Profit Maximizing with a competitive fringe

I have this question: Your business is the dominant firm but there exists a competitive fringe. The competitive fringe produces with total cost: $\; c_𝑓(q_f) = 3𝑞_f$. There have also been some ...
1 vote
54 views

### Extensive Form of Games

Is there any reason for the differing shapes of game trees when we use extensive form representation? For instance, why does the job market signalling game and the repeated Prisoner's Dilemma take the ...
18 views

### PBE solution strategy

I am not comfortable with dynamic games of incomplete info. I am trying to solve the example at https://pubs.aeaweb.org/doi/pdfplus/10.1257/jel.54.2.442 , but can't even come up with a good strategy. ...
99 views

### Perfect bayesian equilibrium on and off the equilibrium path

I know that Bayes's rule can verify the first perfect bayesian equilibria. I am more uncertain about the second perfect bayesian equilibrium, which is off the equilibrium path. Any help would be much ...
36 views

### One shot-deviation property for games of imperfect information

The equivalence between subgame perfection and one-deviation property is typically stated for games of perfect information (where information sets are singletons). Does the Blackwell-style argument ...
1 vote
45 views

### Sequential version of all-pay auction

Sequential version of the all-pay auction. Two bidders alternate in bidding. A prize of \$5 is auctioned. At each move of the game, the bidding player decides whether to raise the current bid by \$1 ...
284 views

### 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 ...
58 views

### 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 ...
1 vote
85 views

### 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 ...
96 views

### 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, ...
65 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 ...
53 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 ...
1 vote
39 views

### 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?
87 views

### 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 ...
1 vote
30 views

### 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 ...
1 vote
39 views

### 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 ...
44 views

### 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 ...
1 vote
776 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' ...
183 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 ...
184 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 ...
528 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 ...
100 views

### 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 ...
128 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 ...
163 views

### 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 ...
127 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 ...
311 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 ...
329 views

### 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 ...
432 views

### 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 ...
1 vote
280 views

### 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 ...
804 views

### 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 ...
236 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 ...
154 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,...
125 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 ...
1 vote
51 views

### 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 ...
1 vote
89 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} &...
1 vote
71 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)(...
71 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 ...
231 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}...
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 ...
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 ...
121 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(...
373 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 ...
148 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 ...
257 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 ...