[abdullahkhalids]

One of my goals is to understand markets through Game Theory. On the producer side, every player can hold, increase or decrease their price. And that changes the rewards for every other player.

What are good references for this?

[worstspotgain]

Assuming low transaction costs and no collusion shenanigans, markets converge in microeconomics even in the presence of market power (meaning producers are big enough that they're not effectively price-takers.) Using Game Theory here kind of complicates the analysis without bringing a lot to the table, unless you have some special conditions or requirements.

If you have an overall demand curve and a marginal cost curve for each seller, you can find the equilibrium where each producer is at their profit-maximization point. In the standard micro textbooks this is the point where each producer's MR is equal to MC, i.e. a local maximum where the derivative of profit with respect to output is zero. [1] In the price-taker case this is easy, as the MR curve is flat. In the non-price-taker case you can just solve iteratively until the whole market converges.

[1] https://en.wikipedia.org/wiki/Profit_maximization

[abdullahkhalids]

I am precisely thinking of oligopolies where either formal collusion happens, or as we often see in the real world, prices going up, without any collusion. In the latter case, the players are using some strategy for switching prices, that leads ultimately to (game-theoretic) cooperation between them.

My understanding is that this a multi-player multi-shot Game, and the methods of game theory can help us understand what the strategy in question is.

[worstspotgain]

Yep, that scenario is (somewhat naively) modeled as an infinitely-repeated Prisoner's Dilemma. The equilibrium in that game is just the monopoly price, i.e. MR=MC for the producers' aggregated MC curve.

So you have the monopoly price at one end (infinitely repeated game, perfect monitoring, no antitrust risk) and the oligopoly price at the other. It's a bit of a castle of cards that's going to fail wildly depending on which assumption you break. If the game is finitely repeated, for instance, the equilibrium is the oligopoly price.

One variant that's been in the news recently is rent-setting software. [1] Here the goal is not running afoul of antitrust. The problem is that it's partly a transaction cost effect, because landlords are publishing rents rather than targeting 100% occupancy (which would make deviating a lot more appealing than colluding for any landlord with less than ~50% of the market.)

If antitrust is not an issue and compliance monitoring is the problem, look for OPEC research.

[1] https://news.ycombinator.com/item?id=41163936

[abdullahkhalids]

I understand what the standard econ calculus based models are. I am a physicist, and we do the same thing where we were really good at modelling systems with small number of particles, or very large number of particles. For small, you can just enumerate all the options, and for large you take the limit to infinity [1], which yields calculus based models.

But a lot of interesting real world systems operate in the intermediate scenario, and I know from physics how 1 or infinity models can fail badly at describing the complexities of intermediate sized systems. In fact, there is a lot of work going on today in various branches of physics in this type of modelling and theory building, because we now have the computational power to understand such systems.

What I am saying about economics are not my original thoughts. I have heard several mathematicians/economists talk about this briefly. I am just looking for the right reference to learn it properly.

[nihzm]

> I am just looking for the right reference to learn it properly.

I once took a course that was mostly based on these two textbooks

- Noncooperative Game Theory: An introduction for Engineers and Computer Scientists (Hespanha)

- Population Games and Evolutionary Dynamics (Sandholm)

Not sure if they are the best place to start but they are definitely solid references that cover game theory (but not much econ). The first one is mostly an introduction to game theory, while the second one is more about what you called "multi-player multi-shot" earlier in this thread, though there is quite a bit of overlap between the two.

[photonthug]

Rent-setting as you mention came to my mind immediately as well. Planet money has a good piece on a related topic https://www.npr.org/2023/02/06/1154775118/ice-cream-ben-jerr... .

This stuff really opened my eyes to the idea that old-school conceptions of things like collusion, and even classic game theoretic ideas of perfect and complete information, all seem to need radical updates for the tightly connected and algorithmic times and economies that we live in.

It seems almost unavoidable that all markets are generally going to move towards both complete and perfect information. We see that this is still somewhat asymmetric, because sellers are more organized because they have more capital, and they can generally afford to hold rather than sell whenever they don't like the market. But in the limit, buyers do catch up a bit, because at least they can browse lots of listings for stuff like housing. Meanwhile in the labor market, the (mostly American) taboo against discussing compensation with coworkers is slowly going away, and there's stuff like glassdoor, and laws that require stating some kind of range for compensation, etc. In terms of cards on the table, people generally can't keep secrets, since we need to account for practically every expense over 10k. Corporations might have an easier time in some cases, but large organizations leak, so I doubt whether they can really hide the fact that they are ramping up for a new chip factory or whatever. So getting a fair price for anything seems likely to get harder, and prices for everything go up.

I'm not versed enough in the topics to really even articulate a good question here, but particularly with more things being algorithmically determined more of the time, perhaps open information is not as good for markets as we thought. Even the relatively straightforward classical idea of a monopoly is starting to feel dated, because if I can own only 10% of 10 key industries and use that to meltdown the whole economy because of the interconnectedness, then focusing on monopolies has little effect on market stability and consumer choice anyway.

Back to the topic of collusion though, maybe the simplest thing is to remove the idea of intent when this stuff is getting litigated. Do we even care that collusion should be some kind of conspiracy with intent? Or do we just dislike the effects and so we want it to never happen? Because in the future human "intent" is going to continue to disappear completely while everyone says "look, the computers decided". There's no cigar-smoking cabal planning stuff in dark rooms anymore because those guys are out golfing. No email chain with a smoking gun, because all that stuff is itself an inefficiency that profit-optimizing algorithms will increasingly be working around.