I’ve started writing a small research paper on this, using mathematical framework, and understood that I had long conflated Shapley values with ROSE values. Here’s what I found, having corrected that error.
ROSE bargaining satisfies Efficiency, Pareto Optimality, Symmetry*, Maximin Dominance and Linearity—a bunch of important desiderata. Shapley values, on other hand, don’t satisfy Maximin Dominance so someone might unilaterally reject cooperation; I’ll explore ROSE equilibrium below.
Subjects: people and services for finding partners.
By Proposition 8.2, ROSE value remains same if moves transferring money within game are discarded. Thus, we can assume no money transfers.
By Proposition 11.3, ROSE value for dating service is equal or greater than its maximin.
By Proposition 12.2, ROSE value for dating service is equal or less than its maximum attainable value.
There’s generally one move for a person to maximize their utility: use the dating service with highest probability of success (or expected relationship quality) available.
There are generally two moves for a service: to launch or not to launch. First involves some intrinsic motivation and feeling of goodness minus running costs, the second option has value of zero exactly.
For a large service, running costs (including moderation) exceed much realistic motivation. Therefore, maximum and maximin values for it are both zero.
From (7), (3) and (4), ROSE value for large dating service is zero.
Therefore, total money transfers to a large dating service equal its total costs.
So, why yes or why no?
By the way, Shapley values suggest paying a significant sum! Given value of a relationship of $10K (can be scaled), and four options for finding partners (0:p0=0.03 -- self-search, α:pα=0.09 -- friend’s help, β:pβ=0.10 -- dating sites, γ:pγ=0.70 -- the specialized project suggested up the comments), the Shapley-fair price per success would be respectively $550, $650 and $4400.
P.S. I’m explicitly not open to discussing what price I’d be cheerful to pay to service which would help to build relationships. In this thread, I’m more interested in whether there are new decision theory developments which would find maximin-satisfying equilibria closer to Shapley one.
I’ve started writing a small research paper on this, using mathematical framework, and understood that I had long conflated Shapley values with ROSE values. Here’s what I found, having corrected that error.
ROSE bargaining satisfies Efficiency, Pareto Optimality, Symmetry*, Maximin Dominance and Linearity—a bunch of important desiderata. Shapley values, on other hand, don’t satisfy Maximin Dominance so someone might unilaterally reject cooperation; I’ll explore ROSE equilibrium below.
Subjects: people and services for finding partners.
By Proposition 8.2, ROSE value remains same if moves transferring money within game are discarded. Thus, we can assume no money transfers.
By Proposition 11.3, ROSE value for dating service is equal or greater than its maximin.
By Proposition 12.2, ROSE value for dating service is equal or less than its maximum attainable value.
There’s generally one move for a person to maximize their utility: use the dating service with highest probability of success (or expected relationship quality) available.
There are generally two moves for a service: to launch or not to launch. First involves some intrinsic motivation and feeling of goodness minus running costs, the second option has value of zero exactly.
For a large service, running costs (including moderation) exceed much realistic motivation. Therefore, maximum and maximin values for it are both zero.
From (7), (3) and (4), ROSE value for large dating service is zero.
Therefore, total money transfers to a large dating service equal its total costs.
So, why yes or why no?
By the way, Shapley values suggest paying a significant sum! Given value of a relationship of $10K (can be scaled), and four options for finding partners (0:p0=0.03 -- self-search, α:pα=0.09 -- friend’s help, β:pβ=0.10 -- dating sites, γ:pγ=0.70 -- the specialized project suggested up the comments), the Shapley-fair price per success would be respectively $550, $650 and $4400.
P.S. I’m explicitly not open to discussing what price I’d be cheerful to pay to service which would help to build relationships. In this thread, I’m more interested in whether there are new decision theory developments which would find maximin-satisfying equilibria closer to Shapley one.