Theory of Model UN — To Merge or not to Merge?

Game Theory and Mergers –It’s Best to Compromise

This article will investigate how Game Theory and particularly the pursuit of Nash Equilibriums justifies the superiority of Compromises at the Merger stage in any competitive MUN scenario. Many pieces on this website have decried the emphasis on compromise in many conferences, observing that such a culture leads to watered-down policy and “phony diplomacy”.

Using Game Theory, this article argues that contrary to popular belief, it is almost always less costly for blocs to merge and then compromise on key issues in order to succeed in this latter phase of MUN. Two ‘games’ can be at play here:

• Neumann’s Game: When Two-Blocs dominate committee, one being nominally “weaker” than the other
• Triangular Diplomacy: A two-step game when three equally sized blocs are vying for supremacy

There are a number of assumptions being made in my case, which I invite you to keep in mind:

This occurs within a highly competitive MUN conference, where all players/blocs are seeking supremacy. Supremacy contained the following components (which I use interchangeably):

• Number of signatories, sponsors, and participants
• Slightly different, the chance such a Bloc will pass their DR.
• Influence of merger participants during the Merger Negotiations: the proportion of bloc-specific clauses successfully included in the final Merged DR; the proportion of Sponsors appointed into the Panel of Authors discussion held during the presentation of the merged DR.

Variables such as Bloc likeability, charisma, diplomatic accuracy and Chair preference, have been excluded and/or mentioned only when necessary. Otherwise, such have an occasional impact on “Supremacy” as mentioned above, and thus have no consequential effect when the theory is repeated enough times.

“Compromise” in this case refers to the act of “sharing supremacy” (usually panel spots or important clauses).

“Conflict” in this case refers to a visible disagreement on the share of supremacy accorded during the merger process.

Additional assumptions will be justified throughout the text.

Neumann’s Game — A Weaker Bloc expresses desire to merge with a more Powerful Bloc

John von Neumann founded Game theory some 88 years ago, having found that two participants in a zero-sum game with perfect information, will always find a pair of strategies in which they can minimize their losses. Nash found that this game could actually be used for an infinite number of participants and under a variety of other conditions, but sticking to two for now.

Imagine you find yourself in Day 2 or 3 of a highly competitive conference, and two major blocs have formed, both with their own Draft Resolutions. Fiery speeches are made by the power-delegates of both blocs but there is a growing sense that they share many common policy suggestions. The weaker bloc decides to invite the power bloc in a merger.

Before this invitation, the stronger bloc had the advantage (let’s say 2 points vs. -1 points for the weak bloc). But now, the weaker bloc placed the strong bloc in a particular pickle:

• Ignore the Merger Invitation: The Weak Bloc stays weak. The Strong Bloc risks looking anti-diplomatic and losing the support of Chairs (who probably want to see collaboration, at least on some level). Let’s say this evens out and the strong bloc gets 0 points vs. still -1 points for the weak bloc. The Cost of Not Merging for Strong Bloc (P) increases (See Tree Diagram next page).
• Participate in the Merger: Where the Stronger Bloc could, if successful, recover 1 point for diplomacy and the gain in numbers (supremacy). If unsuccessful, it would lose a point (-1) for failing to negotiate or act diplomatically with another bloc.

Similarly, for the Weaker Bloc it’s decision to invite the Stronger Bloc for a merger has greatly improved its circumstances and forced the other bloc to engage in a merger. For the Weaker Bloc, it can remain at -1 for failing to Merge, or gain supremacy to 1 point for successfully merging with the more powerful bloc.

As the Stronger Bloc is initially stronger, it will have the upper hand in the Merger negotiations with the Weaker Bloc. It therefore is given the choice to either act conflictually or compromise with the Weaker Bloc (despite the supremacy balance!).

Evidently enough, it is in the Stronger Bloc’s interest to compromise, cede panel spots and key clauses, in order to appear collaborative and obtain the value added of a larger united bloc. If they do so, they will come out strongest with 1 point.

Triangular Diplomacy — Should I Sit and Wait?

In this scenario, you are at the helm of one of three equally sized blocs. You can choose whether you think it’s a good idea to merge with a bloc now or merge later. Merging later assumes that either your two opposing blocs have themselves merged or one bloc has shrunken out of existence.

This is a typical case of Triangular Diplomacy with a spin. You see, the Theory indicates that the third power is not necessarily at an advantage. Rather, it is a combination of timing and execution.

Just like scenario 1, better outcomes emerge from compromise rather than conflict. The best demonstrated path to supremacy is in executing successful compromise-based mergers twice. The second-best option is waiting until the second merger to assert oneself.

To explain. Bloc A, B and C start with equal power. Blocs can choose to remain independent and not merge, but that will incur a -1-point penalty as a result of failing to demonstrate diplomacy and opening dialogue.

Decisions made in the first-merging phase are the same as those in Scenario 1, but influence the scores Bloc A will have in the second-merging phase. For example, Bloc A gets a -1-point score as a result of opting out of a Merge in phase 1, therefore ends up with 0 points after a successful merge with Bloc C.

Taking these scores into aggregate, it is clear that strategies can be ranked in the following order:

1) To Merge with Bloc C after having successfully merged with B

2) To Merge with Bloc C after opting out of merging with B

3) To Opt out of Any Merger Agreement

4) To Merge with Bloc C after failing to merge with B

5) To Opt out of Merging with Bloc C after failing to merge with B.

Conclusion

There is so much talk about the strategies at play in MUN conferences, but noticeably no attempt at generating theory to explain empirical phenomena. Despite the fact that MUN conferences come in many shapes and sizes, Game Theory provides a unique strategic explanation to situations like the Merger Process. It best functions in situations where players of “the game”:

• have access to lots of information
• act rationally
• and offer similar propositions/solutions

The Mergers Phase fulfils these three conditions:

• delegates are encouraged to discover what’s in the policy documents of each bloc and are made aware of the support and size of each bloc via Sponsor/Signatory lists (high information)
• in highly competitive conferences, many delegates act in ways that would advance their country and their own interests
• at the Merger Stage, many papers begin to converge in their propositions (aside from significant policy exceptions) due to the need for each bloc to acquire voting share

The Merger Process is often the most chaotic and complex phase of Model UN debate. Even the most battle-hardened delegates can get lost in its high-pressure and fast paced environment. There is however a set of important elements that could help you navigate through this crucial phase.

Be aware of the fact that your merger strategy has as much to do with strategy as it does with execution. Our second scenario demonstrates this well.

The conventional thinking is that building yourself up with growing numbers through Mergers will help you succeed. Yet only perfect execution on both merger phases delivers a better return than waiting until the second phase to merge.

Conversely, if you are a majority bloc in your committee, you may want to consider merging with other weaker blocs and compromising with them, as the Game Theory shows this delivers far better returns than going at it alone.

Yuji Develle is a Masters student at the London School of Economics & Political Science, Former Media Chair of the United Kingdom and Former President of the King’s College London United Nations Association.