4
votes
3answers
182 views

How practically relevant is game theory?

I usually don't care too much about the practical relevance of nice mathematics :-) But this time, as I am looking to find some areas where I can apply maths and possibly collaborate with ...
2
votes
1answer
137 views

Question on the equivalence of behaviour strategy and mixed strategy for a player with a single information set

Prove that if a player in an extensive-form game has only one information set, then his set of mixed strategies equals his set of behavior strategies. This is the exercise $6.4$ on page $246$ in ...
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
1answer
99 views

Deducing probability of an event, when opponent's type is uncertain

Suppose, two players I and II, given a state space of three states$\{a,b,c\}$ with a common prior, $p(a) = p(b) =p(c) =1/3$, are endowed with two partitions of state space, $\mathscr{P}_\text{I} = ...
1
vote
2answers
452 views

Mathematical Analysis of the Electoral College

Let us consider the electoral college voting system used to elect the American president. I have a few questions from the point of view of decision-making/gaming theory. My ultimate goal is to vote in ...
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, ...