Thank you for your reply—very good point! The “monitoring” and “control” issue may not be a concern, as justified in the “Regarding the Monitor and Control” section.
First, here are some underlying assumptions in the discussion of OCA. OCA is essentially framed within a repeated-game context, meaning that the game unfolds over multiple periods—closely mirroring reality. Additionally, it is assumed that agents know each other’s valuations, which reflects their sophistication or ability to extract value from MEV. In practice, participants might be aware of which actors are best positioned to exploit MEV.
In a one-shot scenario, OCA would be unsustainable because a member could simply breach the agreement by placing a marginally higher bid without worrying about future repercussions or damaging their reputation within the cartel. However, in a repeated game, any breach would eventually be detected (since the outcome changes). In a complete information scenario, the offending member would be caught and thus suffer reputational damage, potentially face expulsion from the game, or be forced to compete against the cartel—outcomes far less desirable than adhering to the agreement in the long run.
Regarding the Monitor and Control:
If I’m not mistaken, your point is that the cartel cannot verify whether the individual responsible for a different outcome is a member of the cartel or an outsider. Even if they know the person is an insider, they cannot determine their exact identity. Furthermore, since the market is open to everyone, outsiders can easily join the bidding process and thus can place a marginally higher bid.
That’s a fair point. However, assuming that agents’ sophistication (i.e., their valuation or ability) in the market is common knowledge, the OCA can still work effectively even if the cartel cannot directly monitor which individual is responsible for a deviation from the agreed outcome.
Let’s consider a simple example below: Consider only three agents in the market at the very beginning—Alice, Bob, and Carol—with sophistication levels satisfying 30 > 20 > 10. It means that if Alice secures the proposing right, she can extract a monetary payoff of 30 dollars. We assume the game is played over infinitely many periods, with each period operating as a first-price auction.
In a single-period non-cooperative equilibrium, Alice will win by bidding 20+\epsilon, \epsilon \to 0. In this case, Alice’s payoff is 30-20=10. If the game is repeated over infinitely many periods and the agents remain non-cooperative throughout, then Alice’s total payoff will be 10 + 10 r + 10r^2+ \dots = \frac{10}{1-r}, where r is the discount factor. Bob and Carol gain 0 all the time.
Alice now announces an OCA: In each period, she submits a bid of a small value—say, 1 (it could be even lower, approaching 0, but for simplicity, we assume 1)—while Bob and Carol bid 0. Then, at the end of each period (after Alice has extracted MEV), she pays Bob and Carol 1 dollar each (also could be even lower). If there is any deviation from the agreed outcome—for instance, if in any period Alice fails to win by bidding 1—the parties revert to the non-cooperative regime.
We assume that agents cannot directly observe the number of bids, meaning they cannot determine whether an outsider has joined. Additionally, if Alice fails to win in a given period, she cannot verify whether the agent responsible for the alternative outcome is Bob, Carol, or an outsider.
Under this OCA, if nobody breaches the agreement, Alice’s payoff is any single period is 30-1-5-4 =20. Alice’s total payoff will be 20 + 20 r + 20r^2+ \dots = \frac{20}{1-r}. Also, since Bob gains 5 dollars in each period, Bob’s total payoff will be \frac{1}{1-r}, and similarly Carol’s total payoff will be \frac{1}{1-r}. Note that all parties receive a higher payoff than they would under the non-cooperative regime.
Will Bob or Carol breach the agreement at any point? They will not, because a breach would reduce their future payoff to 0 from that moment onward, whereas under the agreement they receive \frac{1}{1-r} and \frac{1}{1-r}, respectively. This demonstrates that the OCA can operate effectively even without Monitor.
Now we dive into the Control issue. Based on the above argument, Alice can infer that if she fails to win the bid at any point, it must have been placed by an outsider. How does the Cartel address the outsider problem?
Alice can simply announce a new OCA: For any other agent in the market, as long as that agent, denoted by Dan, with sophistication d, can choose to join the cartel (initially composed of Alice, Bob, and Carol) under the following rule: If Dan can prove that his sophistication exceeds Alice’s, i.e., d>30, then Dan takes the lead. This means that in subsequent rounds, Dan bids 1 while all others bid 0. At the end of each period, Dan distributes payments to Alice, Bob, and Carol—for instance, 1, 1, and 1 dollars, respectively (without loss of generality). If Dan cannot prove that his sophistication exceeds Alice’s, then Alice is still the leader. But Alice has to pay 1 dollar to Dan at the end of each period. Any breach of the agreement results in a reversion to the non-cooperative regime.
Why does the cartel have an incentive to establish this new OCA? It is because the cartel recognizes that, in the long run, they will continually lose if an outsider possesses a higher valuation (sophistication).
Will Dan join the cartel? He will, even if he remains in the dark (i.e., without revealing his sophistication or valuation), because refusing to join would force him to compete against the cartel.
Hence, if Dan’s sophistication exceeds Alice’s—say, 40—he is better off joining the cartel in the long run. This is because, over time, the cartel can gradually raise the bidding price until it approaches 30, meaning Dan would have to bid 30 to win. However, by joining the cartel, he only needs to bid 1 to secure the win and pay 3 dollars (or even less, without loss of generality) to the other cartel members. If Dan’s sophistication is lower than Alice’s—say, 20—he is also better off joining the cartel in the long run. This is because, eventually, he would lose the competition, as he cannot afford to bid more than 20, while the cartel can.
Note that this type of adaptive OCA forms a recursive process. This means that each time the cartel admits a new member, a similar announcement can be made. In the long run, the cartel remains intact, with the most sophisticated agent consistently taking the lead.
Of course, this type of OCA can be applied to other mechanisms as well. For example, similar OCAs can be easily constructed within a Tullock contest. Additionally, forming an entity and cooperating can sometimes enhance their collective sophistication beyond that of any individual (a 1+1>2 effect). Fundamentally, in a long-run setting, lower-sophistication agents naturally delegate their power to the most sophisticated one—just as the saying goes: Leave professional tasks to professionals.
I’ll stop here for now and will revisit your third and fourth points later.