Combinatorial fairness property in division of goods

Given n agents, and m items where vi(g)≥0 is the value of item g for agent i, does there always exist a partition A1,…,An of the m items into n sets s.t. for all i,j∈{1,…,n}: ∑g∈Aivi(g)≥(∑g∈Ajvi(g))−(min Where if A_j is empty, the min is taken as 0. In essence this is a fairness property where … Read more

Game theory of writing multiple choice tests

Here is a model which seems pretty close to my experience of writing multiple choice tests. Let’s view the answer $t$ to each question as a binary string in $S:=\{ 0,1 \}^k$, all equally likely. The scantron sheet offers $a$ answers per question, so the instructor must present the student with an $a$-element set $C$ … Read more

During the game of war, if you could order the cards in your deck of 26, what strategy should you employ? [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 4 years ago. Improve this question During the game of war, if you could order the cards in your deck of 26, what strategy should you … Read more

What are some interesting examples of cooperative games that can be naturally generalised to a stochastic version of it?

In classical, deterministic cooperative game theory, there are $N$ players that can form $2^{N}$ coalitions. Each of these coalitions is assigned a value by means of the characteristic function $v ( \cdot )$ associated with the particular game, such that $v: 2^{N} \to \mathbb{R}$. The game can be “solved” (i.e. the payoffs can be distributed … Read more

How to promote a blog?

Math behind might be interesting. Quite recent bloggingg activity might have interesting math model. The point is that bloggers compete for subscribers and at the same time cooperate gaining subscribers from partner’s blogs. Question is about existence of something like J.Nash’s equilibrium strategy which should balance competition/cooperation. Setup: There are inet blogs, each blog has … Read more

Responses from mathematicians concerning Flash trading [closed]

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for … Read more

All solutions to a set of integral equations

I would like a better understanding of the set of pairs (f1,f2) of functions [0,1]×[0,1]→[0,1] which satisfy the following conditions: For all y∈[0,1], f1(x,y)≥f1(x′,y)⇔x>x′. For all x∈[0,1], f2(x,y)≥f2(x,y′)⇔y>y′. f1(x,y)+f2(x,y)=1, for all (x,y)∈[0,1]×[0,1] f1(x,y)=f2(y,x) for all (x,y)∈[0,1]×[0,1] Due to monotonicity (Condition 1), the functions f1 and f2 are integrable. Now define p1(x,0)=xf1(x,0)−∫x0f1(t,0)dt, p2(0,y)=yf2(0,y)−∫y0f2(0,t)dt, p1(x,y)=p1(x,0)+xf1(x,y)−∫x0f1(t,y)dt, p2(x,y)=p2(0,y)+yf2(x,y)−∫y0f2(x,t)dt. Then … Read more

How many different states of Nash equilibrium?

So there is this quite well known Prisoner’s dilemma where two parties can both defect and cooperate (and get points based on their decisions). In my presently used example I take it that cooperating player always gets 2 points while defecting player gets 3 points against cooperating opponent and 0 points against defecting opponent. So … Read more