0
votes
1answer
53 views

Game Theory and Uniform Distribution question?

In an Auction , two players are bidding. Their bids will be a unknown fraction of their valuations. The valuations come from a uniform distribution $$[0,1] $$ If Player 2 bids $$ v/2 $$ and Player ...
2
votes
1answer
94 views

Unbalanced game: probability of winning over an infinite number of possible match sequences

We have 2 players, A and B, competing. The probability that A wins a match is p, making the probability that B wins a match (1-p) = q. The game is won by player A as soon as he gets one more win than ...
13
votes
3answers
2k views

The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go. A suitably robust argument that establishes what is statistically the best strategy will be accepted.] Here's my description of the game: There's a $4\times 4$ ...
2
votes
1answer
54 views

Deriving statistical distributions from games

The normal distribution can be derived from basic principles and calculus The Normal Distribution: A derivation from basic principles. Are there other distributions that can be derived like this from ...
1
vote
1answer
49 views

Number of rounds to find out the winner in nondeterministic game

Imagine, I'm organizing competition for AI Yahtzee players (or some other game, poker, backgammon etc.). I want to find out who plays better: player A or player B. If they play just one game, winner ...
1
vote
1answer
65 views

simultaneous probability elicitation from multiple agents without an exogenous banker

A proper scoring rule is a function $f:[0,1]\times\{0,1\}\to \Bbb R$ such that, if a subject will receive a reward of $f(x,0)$ for reporting his estimate of the likelihood of an event as $x$ if the ...
0
votes
3answers
115 views

How to discourage contestants from entering a lottery twice?

Suppose you have a lottery. And you want to prevent participants from buying multiple tickets. What would be the best way to discourage this? For example, increasing the win-chance for all previously ...
4
votes
2answers
192 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
1
vote
2answers
170 views

Is risk-taking a zero-sum game?

I learnt that trading is a zero-sum game since profits take out losses while holding your assets may not always be a zero-sum game when time passes and everybody's assets theoretically can grow in ...
0
votes
1answer
102 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
2
votes
1answer
159 views

Game Theory: determining the value of the foxhole game

"A soldier can hide in one of five foxholes, and a gunner can hide in four spots: A, B C, and D. The configuration looks like this: 1 (A) 2 (B) 3 (C) 4 (D) 5. If a shot is fired at a location and the ...
1
vote
2answers
362 views

Game theory: Nash equilibrium in asymetric payoff matrix

I have a utility function describing the desirability of an outcome state. I weigh the expected utility with the probability of the outcome state occuring. I find the expected utility of an action, a, ...
1
vote
0answers
181 views

On a zero-sum game betting market

I'm trying to come up with the rules for a betting game. My problem is to figure out under what constraints that game has zero-sum game properties: in other words, I want to make sure that no money is ...
2
votes
0answers
106 views

proof using (fixed point theorem)

I am seeking to solve for a Nash equilibrium in pure strategies $(d_2,d_2)$ involving two players, $1$ and $2$. Given that $h'(.)$ is s strictly decreasing and continuous function, $\Phi(d_1-d_2)$ ...
0
votes
2answers
216 views

Given a victory condition and a set strategy, what are the chances of winning on a given turn in a game of Magic: The Gathering?

Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very ...
6
votes
1answer
180 views

How to find a flat using game theory?

I had the idea that maybe probability/game theory knowledge helps finding a flat more systematically. I assume that I have some online offers with number parameters: prize size (square meters) ...