0
votes
1answer
26 views

Maximum payoff for safe bet

I'm having a hard time choosing a good strategy for this problem: assume that you have $m$ money that you can bet on $n$ mutually exclusive outcomes, all with unknown probabilities, and that each ...
0
votes
0answers
13 views

Dual proof in Zero sum games

Say Player 2 is $P: max \sum_1^n x_j $ subject to $Ax \leq b$. I believe the Dual problem for this would be $D: min \sum_1^n y_j$ subject to $A^T y \geq 1$. Player 1's problem would be $max \{min ...
1
vote
1answer
41 views

need help with zero sum game

Tom chooses an integer in {1,2,3} and Bob chooses an integer in {2,3,4}. If the chosen numbers are the same, no money changes hands If the numbers are different the person who picks the bigger number ...
2
votes
1answer
60 views

Solving a 3x3 payoff matrix

I need some help solving the value of this payoff matrix and finding the optimal strategy: $$ \begin{matrix} 1 & 2 & 4 \\ -1 & 5 & 3 \\ 3 & 3 & ...
0
votes
0answers
24 views

Value of Zero-Sum Game

My question is the following: Let $A \in Mat_{n}(\Bbb R)$ be the payoff matrix for player 1 in a 2-player zero-sum game, and suppose that $A$ is invertible, symmetric and such that $A^{-1} e \ge ...
1
vote
0answers
21 views

Matrix multiplication in game theory doesn't add up? Min y^T*Ax

I'm studying game theory and something seems weird to me. My book says y is the probability of the row player and x is the probability of column player, both x and y are vectors. A = [a$_i$$_j$] is ...
1
vote
0answers
25 views

Prove the partial derivative of the summation of $$(y-g_i+a\sum^n_{j=1} g_j)=-1+na >0$$

I have a function: $$\pi_i^1=y-g_i+a\sum^n_{j=1}g_j,$$ where 0 < a<1< na, and I need to prove this: $$\frac{\partial(\sum^n_{i=1}\pi^1_i)}{\partial g_i}=-1+na>0.$$ I am not very ...
12
votes
3answers
553 views

Formula for picking time closest to (but after) target

Let's say you have an arbitrary length of time. You are playing a game in which you want to push a button during this time span after a light comes on. If you do so, you win ($+1$), if not, you lose ...
3
votes
1answer
77 views

Effecient way to find optimal solution in a 2 player game

I have a function: \begin{equation*} f(a_1,\ldots,a_7,b_1,\ldots,b_4)=-14-7 a_1+30 a_1 a_2-7 a_4-2 a_4 a_5+21 a_6+21 a_7+16 a_1 b_1-24 a_1 a_2 b_1+6 a_4 b_1-6 a_4 a_5 b_1+6 a_1 b_2-6 a_1 a_2 b_2+8 a_4 ...
0
votes
1answer
160 views

Solving a linear programming problem: Are my formulations correct?

QUESTION J (PTY) LTD is a fertilizer manufacturing enterprise that produces two types of fertilizers, namely white and gray. The white fertilizer is for crops like maize, sorghum, etc while the gray ...
0
votes
1answer
62 views

Correlated Equilibrium

I have a question about the definition of the correlated equilibrium. I see that some authors define it as "expected payoff of playing the recommended strategy is no less than playing another ...
11
votes
2answers
133 views

Fastest way to get \$1 million of two different currencies in a video game

This question actually relates to a video game, I came across the scenario and I realized I had no idea how to go about solving something like this or even what branch of mathematics it falls under. ...
0
votes
3answers
123 views

How to write “the parameter maximizing the maximum of the maximum value of two functions continuous in the domain of maximization”

Say you have $f(x),g(x)$ continuous where they need to be and you want to express the following: Give me the biggest value of $f$ for $x \leq X_f$ , give me the biggest value of $g$ for $x \leq X_g$, ...
1
vote
1answer
111 views

Modellering a Integer Linear Program

Warning; !! Long post !! Note; This is not a homework assignment, but rather an old exam question I'm trying to figure out. If you read on, you'll notice that I've put quite some work in on it ...
1
vote
1answer
145 views

Goofy problem: Optimal bet with nearly no knowledge

A year or so back, on the verge of falling asleep, I thought up this question: You have come to me ready to gamble. I have two envelopes on the table, one containing the amount of my bet, and one ...
0
votes
0answers
24 views

Congestion Game with Varying Price

I molded my problem as the following game (it is a congestion game with varying price): $N$ players share resources $E$, $S_i$ is the strategy space of player $i$ which is in $2^E$ (where $2^E$ is ...
2
votes
0answers
156 views

A dynamic Stackelberg game - general characterization

my question is about general representation of a dynamic Stackelberg game which is played in continuous time. We have maximization problems of two agents who play this game. Agents are 'Leader' and ...
1
vote
0answers
57 views

Parameterized convex optimization

I'm trying to formulate a game so that at Nash equilibrium I achieve supply equales demand. Then I ran into this problem. For all $i,$ $v_{i}\left(x_{i}\right)$ is concave in $x_{i}$. The value ...
0
votes
1answer
78 views

Solution for assigning independent tasks to independent individuals

I have $n$ tasks that I wish to delegate to $m$ independent individuals, where $m$ is a factor or divisor of $n$. Each of the tasks $T_{1} ... T_{n}$ is independent. From the following two extremes, ...
0
votes
2answers
94 views

value of this possibly Monty Hall-related 2-person zero-sum game?

Player A tosses a fair coin. He knows how it lands; Player B does not. A can now play move 1 or move 2. If he plays move 1, he pays B £1. If he plays move 2, then B can either play move X or move Y. ...
0
votes
1answer
202 views

Nash Equlibria and Maximin Strategies

Consider the following bimatrix game $(2,6)\ \ \ (4,2) \\ (6,0) \ \ \ (0,4) $ I have been asked to compute all equilibria of this game, as well as the maximin strategies for both players. Now I used ...
2
votes
1answer
71 views

game strategy question

Let's say there are doors each with a lock on the integral points ($0$, $\pm1$, $\pm2$, $\cdots$) of the line. You are given a key which can only open a single lock, but you are not told what lock the ...
0
votes
1answer
221 views

Payoff of a unilateral deviation in an $n$-player zero-sum game

In a $n$-player zero-sum game, one of the players, say $k$, unilaterally deviates from her Nash equilibrium strategy while all the other players stay on the equilibrium. Now, we all know that $k$'s ...
2
votes
1answer
89 views

Game Theory Moving Around Coins

To start off, we have coins arranged in the following order: ..C.. A F.. D.. B ..E.. G The goal of this game is to return these letters into alphabetical order: A, B then C, D, E then F, G in the ...
5
votes
1answer
28 views

Mechanism to auction off multiple resources given fixed budgets

I am trying to sell ad time on a screen to a bunch of advertisers. The advertisers tell me (or a salesperson keys in) how much a given advertiser is willing to pay for time in a one hour block. Each ...