Comment by jmward01
1 day ago
One thing I have always thought was missing in game theory (and it is probably there but I just haven't looked hard enough) is a mathematical framework for how to build trust to increase the infinite payout for everyone. If in the decision making the idea of an offering is added in then it brings up the possibility of gauging trust and building trust so that future actions can capture more value until an optimal infinite policy is attained. So, for instance, I look at all my possible options and I choose one based on how much I trust the other party AND how much I want to increase that trust in the future. So I give them an offering, select an option that gives them a little more but at a cost to me, to prove that I am willing to increase trust. If they reciprocate then I loose nothing and the next offering can be bigger. If they don't then I gained knowledge and my next offering is smaller. Basically, this is like tit for tat but over time and intended to get to the optimal solution instead of the min max solution. Clearly I'm not a mathematician, but I bet this could be refined to exact equations and formalized so that exact offerings could be calculated.
With an optimal way of determining fair splitting of gains like Shapley value[0] you can cooperate or defect with a probability that maximizes other participants expected value when everyone act fairly.
The ultimatum game is the simplest example; N dollars of prize to split, N/2 is fair, accept with probability M / (N /2) where M is what's offered to you; the opponents maximum expected value comes from offering N/2; trying to offer less (or more) results in expected value to them < N/2.
Trust can be built out of clearly describing how you'll respond in your own best interests in ways that achieve fairness, e.g. assuming the other parties will understand the concept of fairness and also act to maximize their expected value given their knowledge of how you will act.
If you want to solve logically harder problems like one-shot prisoners dilemma, there are preliminary theories for how that can be done by proving things about the other participants directly. It won't work for humans, but maybe artificial agents. https://arxiv.org/pdf/1401.5577
[0] https://en.wikipedia.org/wiki/Shapley_value
Thanks. I'll take a look!
There's certainly academic work about game theory and reputation. Googling "reputation effects in repeated games" shows some mentions in university game theory courses. There's also loads of work about how to incentivizing actors to be truthful (e.g. when reviewing peers or products).
Signaling theory (in evolutionary biology) might also be vaguely related.
This is the TCP backoff algorithm, specifically the slow start to find the optimal bandwidth. In your analogy, it would find the optimal amount that a person is willing to reciprocate.
Not only does this algorithm exist, but we're using it to communicate right now!
https://en.wikipedia.org/wiki/TCP_congestion_control
I have noticed this algorithm in many places which is why I think it is a missing piece in game theory and why formalizing it could be powerful. People use this instinctively in their interactions with others and algorithms (like the one you pointed out) have been created using the basic concept so a formalization of the math is likely in order. Consider the question of how big the offering should be. What if all parties are actually getting the optimum result, what mechanism stops the increase/why? Does it stop? Could this lead to both parties paying the other larger and larger sums forever? It is a fun thing to think about at least.
Yes, this is AIMD and it's well formalised and understood.
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Look into cooperative game theory. If I remember correctly, trust is modelled as a way of exchanging information and influencing the probabilities that other players place on your next action
Nature already solved that and implemented it. It's all around us with relationships. Not just among humans. They typically last over a single interaction. Especially if you don't ignore the rules of the game.
But the game theory of nature also leaves room for other sort of players to somehow win over fair play. I thought this was a bug but over time realised it is a feature, critical to making players as a whole stronger. Without it there would be no point for anyone to be creative.
If you can solve the issue and make a playbook so that everyone do tic for tac, it won't take long for a bad actor to exploit it, then more, then you are back to where we are now.
I think this comes down to the fact that we can keep a mental ledger on the reputations of 50–100 people, so our in-built reputation system breaks down at the current scale.
You could try building a social credit system to scale things up, but that tends to upset people...
Social credit systems upset people because of distrust in the system operators.
Do you have an example of this in mind where the known "tit for tat" strategy falls short?
I don't have a concrete example, but I think you can invent plenty of iterated prisoner's dilemmas with whatever modified rules and variables and find 'tit-for-tat' isn't the end-all-be-all. Like it changes things if there's an infinite or an unknown number of rounds, some of the defects are 'noise', etc.,.
Economist here (but not a game theorist): Repeated games are actually really hard to find closed form equilibria for in general. Additionally, many repeated games have multiple equilibria which makes every bit of follow on analysis that much more annoying. Only very specific categories of repeated game have known nice unique solutions like you are hoping for, and even then usually only under some idealized information set structure. But as other commenters have said, this is an active area of research in Economics and many grad classes are offered on it.
I wouldn't put so much stock in a mathematical model like game theory.
Humanity has accomplished a lot with the notion of number, quantity, and numerical model, but in nearly all these cases our success relies on the heavy use of assumptions and more importantly constraints—most models are actually quite poor when it comes to a Laplacean dream of fully representing everything one might care about in practice.
Unfortunately I think our successes tends to lead individuals to overestimate the value and applicability of abstract models. Human beings are not automatons and human behavior is so variable and vast that I highly doubt any mathematical model could ever really account for it in sufficient detail. Worse, there's a definite quantum problem. The moment you report on predicted behaviors according to your model, human beings can respond to those reports, changing their own behaviors and totally ruining your model by blowing the constraints out of the water.
I actually believe that many of humanity's contemporary social issues actually stem from overreliance on mathematical models with respect to understanding human behavior and making decisions about economics and governance. The more we can directly acquire insight into individuals rather than believe in their "revealed preferences" the better off we'll be if we really want a system in which people's direct wants are represented (rather than telling them "you say you want X but when I give you only Y as choice you choose Y so you must want Y"—it's totally idiotic).