So, here's what we, game theorists, mean when we say, "collusion." Think of a market with two firms. If one firm charges less for the same product than the other, consumers will patronize the firm charging less money, so unless there's something fishy going on, the firms should both charge a price set by the intersection of the supply and demand curves. (Remember Econ 101? Or maybe it's 102 here. Whatever.) However, what if both firms decide to jack up their prices by the same amount? Some customers drift away because of the elasticity of demand, but at a higher price per unit, each firm makes more total profit, and as long as both firms raise their prices by the same amount, neither firm undercuts the other. Each firm still gets a 50% market share.
This is called "price-fixing," and it is a violation of anti-trust law. When we model it with game theory, it looks just like the prisoner's dilemma. Each firm has two options-- raise prices, or keep prices low. They make their decisions simultaneously. If you keep your prices low, I have to do likewise or I'm priced out of the market. If you raise your prices, I'd rather keep my prices low to price you out of the market. No matter what, my best strategy is to keep my prices low. The game is symmetric, so the same holds for you. We each need to keep our prices low. However, the Pareto efficient outcome, from the firms' perspective, is to raise prices. They just can't get there in equilibrium in a one-shot game. That's a prisoner's dilemma.
Like a prisoner's dilemma, the solution is repetition. Each firm incrementally raises their prices just a tad, followed by the other firm raising their prices a tad. Tit-for-tat price-fixing. If you want to read a good book on tit-for-tat cooperation in the prisoner's dilemma, try Robert Axelrod's The Evolution of Cooperation.
And we have a term for this behavior, among price-fixing firms. "Collusion!"
Sorry, missed the caps-lock. Lemme try that again. "COLLUSION!!!" There. That's better. Price-fixing agreements are "collusive" agreements. In the law, it's all about anti-trust violations, and price-fixing, but in game theory, we really do talk about "COLLUSION!!!"
And note how it happens. In game theory, we don't give a rat's ass about the players talking to each other because talk is cheap. Players signal to each other through their actions, especially in repetition. Firms engaged in price-fixing, or, sorry... "COLLUSION!!!," will never write memos to each other specifying the arrangement. They'll just sequentially, incrementally jack up their prices in response to each others' price increases.
And yes, it's illegal, but what are you going to do about it? You can't prosecute for this. Why not? All the firms need is anything resembling an excuse. Each firm is facing their own internal pressures for price increases. Internal costs, pressure from stock-holders, blah, blah, whatever. Prosecuting would require the kind of communication and direct arrangement that, in game theory, our goal is to disregard anyway! The whole point of studying this in game theory is to acknowledge that talk is cheap and see what you can derive when people don't talk.
And no talking means nothing to use in court, but we, in game theory, still call it "COLLUSION!!!" Why? Because sometimes, my colleagues in game theory don't have their heads completely up their asses. Sometimes.
The basic point is that price-fixing is illegal. Any of this kind of "collusive" agreement is illegal. So... don't put it in writing, or talk about it in such a way that you can be prosecuted for it! Come on! How hard is this? Collusion, in game theory, is a process that is implicit, and arranged and signaled through actions, but by divorcing it so thoroughly from any communication, the actors accomplish a critical goal-- making it impossible to prosecute what they are doing because it is, as mentioned... a crime.
What's amazing here is just how far the Trump campaign and Russia went. That Manafort/Kilimnik meeting... WOW. That was STUPIDLY brazen. That's absolutely "collusion." Criminal conspiracy? If two firms sequentially raise their prices in response to each other, you can't nail them for price-fixing because they'll each make up some bullshit reason, and they just need something as a reason. Bullshit or not, they'll get away with it. Price-fixing is almost impossible to prosecute, which is why we really don't like oligopolies. If we had real enforcement for price-fixing, we wouldn't care about the number of firms in a market as long as it's more than one, and even then, the threat of entry could keep a monopoly in line (yes, I am greatly oversimplifying). The reason we care is that nobody can ever prosecute this stuff.
Collusion versus criminal conspiracy. Understanding the game theory here, how collusive agreements develop, how we study them in game theory... this matters. We use the term, "collusion," all the time in game theory, and the distinction between its use in game theory and in its analogous place in the law demonstrates exactly the problem here.
Well, problem from our perspective, and by "our," I mean, "America's." This is great for Russia, and by, "Russia," I mean, "Donald J. Trump." Yes, he "colluded." It is vital to understand the difference between "collusion" and "criminal conspiracy." One term is legalese. The other has actual meaning to human beings.
Now, countdown to Manafort's pardon, after having given Konstantin Kilimnik exactly what the Russians wanted in a "collusive" action. Anyone who wants to convince me of "NO COLLUSION!!!" still needs to give me a non-collusive explanation of that meeting. Just because it isn't prosecutable as "criminal conspiracy" doesn't mean it isn't collusion by any coherent definition of the word.