Background

Are there rational explanations behind the seemingly irrational actions in the Russo-Ukrainian war? Can those same explanations be used to forecast upcoming political and military actions in the crisis? And what actions might lead the war to escalate to a nuclear conflict?

Those were big questions in my mind back in October 2022. At that time, the Russo-Ukrainian war’s path was uncertain: Ukrainian forces appeared to have a slight advantage on the ground, but Putin had just ordered the partial mobilization of 300,000 troops, and both Russia and NATO had exchanged nuclear threats.

October 2022 also marked my turn to host ‘Article Club’, a recurring get-together with some Seattle friends. For the topic of my turn, I proposed ‘theories of conflict escalation and implications for the Russo-Ukrainian war’. During my research, I was surprised (and relieved) to find that theory suggests that geopolitical conflicts rarely spiral out of control. Instead they follow intentional and defined sequences [1]. Furthermore, the progression of those sequences can be explained using game theory. Assumptions are made on rationality by considering payoffs to both the participating states and the leaders themselves. In particular, I was interested by Kahn’s model – and metaphor of a ladder – to explain the escalation of the Cold War between the US and USSR [2].

I created a game to apply these theories of conflict escalation and see if rational, impartial actors (i.e. my friends at Article Club) would take the same actions as the political leaders in the Russo-Ukrainian war. The key principles of my game design were as follows:

• There are two teams ('factions'): a Russian team and a NATO team (note: future versions of the game could consider a three-party conflict by splitting Ukraine from the NATO team, to better reflect their distinct interests).
• The participants, organized into the two teams, needed to have 'skin-in-the-game' by buying into the game with real money.
• Teams would compete for the same pot of money and earn payoffs based on their actions. 
• Teams would be aware of the ‘rungs of the ladder’ (representing the level of escalation), but not the specific payoffs of actions possible at each rung.
• The Russian team would have, in total, a negative expected payoff following the start of the war (i.e. the further the conflict progresses, the more money they are bound to lose). But, the Russian faction would also have little incentive to de-escalate at any particular stage in the crisis because, at each turn, they would have an action available that could win them more money.
• There would be no Nash equilibrium (i.e. on any turn, there would always be more money to be gained by one team by either escalating or maintaining status quo).

The outcome of our game, while not inevitable, was all-out nuclear war. However, this was largely a function of the relatively low stakes of the game. The buy-in for our game was $20 and the total pot size was $240. Even so, Putin’s actor became rightfully cautious of losing their stake of the pot once an action of theirs came with a 25% chance or greater of being overthrown. Ultimately that risk was not enough to discourage escalation, as losing $20 is a much different proposition than losing one’s title or life in reality.

We came away from the game with an understanding that actions in the Russo-Ukrainian war could be rationally explained. Additionally, we were moderately reassured by the notion that the crisis would be unlikely to escalate to a general nuclear conflict, as long as there remains a significant risk of Putin being overthrown.

Below, I have outlined the game rules so that others can play the game or even modify the rules themselves.

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Overview

In this game, you act as factions (either NATO or Russia), competing for victory in the Russo-Ukrainian war (circa February 2022). Your role, as political leaders, will be to assess, negotiate and ultimately decide on actions to take in the crisis. In general, actions will either deescalate, maintain the status quo or escalate the crisis. But beware, your opponent will be doing the same as well.

Objective

To earn the highest payout for yourself and your faction, while avoiding the risk of losing it all by either being overthrown or having the crisis escalate to an insensate nuclear war.

Contents

• 1 main board (see image below), which tracks the current stage – or ‘rung’ – of the crisis, the payoff scale, and the risk of Putin being overthrown.
• 125 cards (see images below), which outline the actions available to a team at a particular rung of the crisis and the potential payoffs of that action (refer to table below).
• 2 dice, to determine if Putin is overthrown on a particular action.
• 1 coin, to determine whether the low or high payoff of an action is granted.

Setup

1. Nominate a game facilitator, who does not participate in the game as a member of a faction.
2. Have each participant pay a sum of money to the game facilitator, who will hold the funds in escrow until the game ends.
3. Sort the participants into the NATO and Russian factions.
4. Randomly assign the role of Putin to a player on the Russian team.

How to Play

Gameplay is turn-based, with the first turn of the game being presented to the Russian faction. Payoffs are recorded on a percentage-based scale (-100% to 100%) which represents the relative additional amount of the pot assigned to the leading faction (refer to ‘How the Game Ends’ below).

1. The game facilitator hands out three cards, corresponding to the de-escalatory, status quo and escalatory actions at that stage of the game for a particular faction.
2. The faction can negotiate both internally and externally prior to deciding on an action.  
3. The act of deciding on an action differs by faction: NATO must approve the action via a majority vote, while Russia simply needs Putin to approve the action.
4. Once an action is decided, resolve the random elements of that action, if necessary:
   1. If the action has two possible payoffs, then a coin is flipped to determine whether the low or high payoff is assigned.
   2. If the action comes with risk of Putin being overthrown, it is determined by rolling dice. If Putin is overthrown, then that player loses their share of the pot (the Russian pot is now divided amongst one fewer participants), a new participant is randomly assigned to be Putin and can decide whether to go through with the action.
5. The game facilitator then applies the net incremental payoff for that action to the payoff scale on the main board.
6. The game facilitator also adjusts the rung of the ladder on the main board based on the action taken by the faction if it is de-escalatory (reduce rung number by 1) or escalatory (increase rung number by 1).
7. The game facilitator then hands out the three cards corresponding to the new stage of the game to the other faction.
8. Steps 2 to 7 are repeated until the game ends.

How the Game Ends

The game can end at any time via negotiation. In that case, the payoffs are determined as follows:

• Faction A payoff = (| Final payoff scale % | / 200% + 50%) * Pot size
• Faction B payoff = Pot size – Faction A payoff
• Participant payoff = Faction payoff / number of (non-overthrown) faction participants

However, if the Russian faction payoff percentage is negative at the game end, then Putin's actor must flip a coin to determine if he or she is overthrown, prior to the game ending.

Finally, if the game progresses to insensate nuclear war (rung 21), then each faction flips two coins simultaneously to determine the payoffs, as follows:

	Faction A Heads	Faction A Tails
Faction B Heads	Split the pot 50/50	Faction B wins 100% of the pot
Faction B Tails	Faction A wins 100% of the pot	Both factions lose and the game facilitator keeps the pot.

Appendix

[1] https://www.jstor.org/stable/pdf/10.7249/mg614af.9.pdf, https://link.springer.com/content/pdf/10.1007/978-94-6265-419-8.pdf

[2] https://wiki.baloogancampaign.com/index.php?title=Kahn%27s_Escalation_Ladder, https://www.jstor.org/stable/10.7249/j.ctt1cx3vg8.9?seq=1#metadata_info_tab_contents, https://www.rand.org/blog/2022/04/book-review-escalation-and-deescalation-of-crises-armed.html

Figure 1) Main Game Board

Table 1) All of the actions for each faction at each rung of the crisis, the payoffs of those actions, and the risk of Putin being overthrown. This information is transferred to the game cards, shown below.

Rung	Description	Russia - Escalation	Russia - Status Quo	Russia - De-escalation	Putin Overthrow Risk	NATO - Escalation	NATO - Status Quo	NATO - De-escalation
0	Local mobilization	(+20,+50) | Initiate "Special Military Operation"	(0) | Build-up troops on the border of Ukraine	(-10,0) | Send troops home	-	- | -	(+5) | Train and build-up troops	- | -
1	War	(+5,+10)  | Restrict gas flow to Europe with pipeline "maintainance"	(-5) | Continue "Special Military Operation"	(-10,-5) | Withdraw troops	-	(+5, +15) | Impose sanctions on Russian trade	(+5) | Let Ukraine fight on their own	(-20,-10) | Convince Ukraine to surrender
2	Sanctions	(+5,+10) | Make nuclear threats	(-5) | Continue to conduct gas pipeline "maintenance"	(-15, 0) | Resume gas flow	-	(+5, +10) | Conduct nuclear exercises	(+5) | Impose sanctions on Russian elite	(-10,0) | Relax sanctions
3	Threaten	(+10,+15) | Shell Zaporizhzhia nuclear plant	(+5) | Demonstrate the number of nukes in possession	(-10,-5) | Recoile on nuclear threats	-	(+5, +20) | Send Stinger missiles to Ukraine	(0) | Biden states, "[Tactical nuke could lead to] Armageddon"	(-5, 0) | Halt nuclear exercises
4	Mass convential warfare	(+5,+15) | Attack and massacre civilians in Bucha	(+5) | Partial mobilization	(-15,-5) | Halt shelling on key infrastructure	-	(0, +20) | Send HIMARS	(+5) | Send limited range artillery	(-10,-5) | Stop sending weapons to Ukraine
5	Attack civilians	(+20,+25) | Annex Ukrainian territory	(+10) | Honor Bucha army division	(-15,-10) | Criticize Bucha army division	-	(+5, +10) | Provide tanks	(+5) | Issue UN War Crimes Resolution for Russian conduct	(-15,-5) | Stop provision of advanced weapons
6	Legal territorial claim	(+5,+10) | Issue nuclear ultimatums if territory is threatened	(+5) | Displace civilians in annexed territory	(-15,-10) | Clarify (and reduce) the legal territorial claims	-	(+5, +15) | Firm deterrence (e.g. state that tactical nukes will result in retalitory strikes)	(+10) | Continue offensive on annexed Donetsk territory	(-20,-10) | Halt attacks within annexed territories
7	Nuclear ultimatums	(+5,+10) | Ready nuclear forces and put on high alert	(0) | Warn of "uncontrolled escalation"	(-10,-5) | Clarify that nukes will only be used reactionarily	-	(+5,+15) | Ready nuclear forces	(+5) | Issue continued nuclear retalitory threats	(-10,-5) | Claim neclear threats were accidents
8	Ready local nuclear forces	(+25,+35) | Tactical nuclear strike on Snake Island	(+5) | Move warheads closer to front	(-25,-15) | Standdown nuclear forces	-	(0,+30) | Guide a missile into the Black Sea	(+10) | Ready and reposition nuclear missiles in EU	(-20,-10) | Stand down nuclear forces
9	Exemplary strike	(+15,+20) | Declare legitimate use of tactical nuclear weapons in Ukraine	(+10) | Tactical nuclear strike in forest	(-20,-10) | Claim launch was accidental	8.3%	(+25,+35) | Declare pre-authorization of a retalitory strike against Russia	(+30) | Launch missiles into the Baltic Sea	(-15, -5) | Claim the launch was accidental
10	Declaration of limited nuclear war	(+5,+10) | Evacuate 5m RU citizens from RU-UK border	(+5) | Define limits of nuclear war to only Ukraine	(-40,-20) | Declare end to limited nuclear war	-	(+5, +15) | Evacuate ~30M Ukranian citizens from cities	(+10) | Define limits of nuclear use	(-20,-10) | State that NATO will not use nukes in response to the war in Ukraine
11	Evacuate local citizens	(+10,+15) | Launch tactical nuclear weapon on airbase	(+5) | Evacuate 2m more civilians near border	(-10,-5) | Send civilians home	-	(+20,+25) | Destroy the Black Fleet	(+15) | Evacuate ~6m citizens from Baltics	(-10,-5) | Send civilians back home
12	Exemplary strike on Military	(+20,+25) | Launch tactical nuclear weapon on Bahkmut	(+10) | Launch tactical nuke on naval base	(-15,-10) | Seek nuclear ceasefire	16.7%	(+25,+35) | Launch missiles on Russian supply chains	(+15) | Destroy Crimean military bases	(-15,-5) | Seek missile and nuclear ceasefire
13	Exemplary strike Against Population	(+5,+15) | Evacuate RU citizens from St Petersburg and Moscow	(+5) | Strike Kherson with a tactical nuke	(-10,-5) | Claim strike on city was accident	-	(+15,+25) | Evacuate citizens from EU cities	(+10) | Launch cyberwarefare attack on Russia	(-10,-5) | Claim strikes were accidental and meant for military targets
14	Complete Evacuation	(+5,+15) | Prepare for highest nuclear readiness level	(0) | Evacuate from all major cities	(-10,-5) | Send all citizens home	-	(+10,+20) | DEFCON 6	(+5) | Evacuate US citizens from cities close to military targets	(-10,-5) | Send all citizens home
15	Complete nuclear force readiness	(+30,+45) | Formally declare war against NATO and full mobilization (no nukes)	(+5) | Remain on highest alert and re-position nukes	(-10,-5) | Standdown nuclear forces	-	(+15,+20) | Formally declare war against Russia	(+10) | Reposition US nuclear missiles	(-15,-10) | Stand down nuclear forces
16	Formal declaration of general war (but w/o general nuclear use)	(+20,+25) | Strike NATO supply routes in Europe	(+15,+20) | Mobilize all civilians	(-30,-5) | Seek ceasefire	27.8%	(+25, +35) | Strike Russian airbases in Europe and around Ukraine	(+15) | Call up US reserves	(-30, -5) | Seek ceasefire
17	Counter property war (tit-for-tat)	(+30, 35) | Launch strike on military bases in Baltics	(+10) | Strike NATO ports and naval yards	(-25,-20) | Do not return missile fire	-	(+20, +25) | Strike all Russian Arctic and Baltic naval bases	(+5) | Destroy supply routes to and from Kaliningrad	(-25,-20) | Only take defensive actions
18	Major disarming strike (but not on city)	(+40,+50) | Invade Finland	(+20) | Strike military bases in Greece	(-20,-10) | Do not return missile fire	-	(+20,+40) | Invade Russia from Finland	(+25) | Strike minor Russian missile silos	(-25,-15) | Do not return missile or tactical nuke fire
19	Major land invasion	(+40, +50) | Lunch a strategic nuke against Kyiv	(+20) | Invade Estonia	(-25,-20) | Withdraw troops	41.7%	(+50,+60) | Launch a strategic nuke against Kozelsk and all known major nuclear silos	(+30) | Attack through Belarussian front	(-30, -20) | Withdraw troops
20	Strategic nuclear use	(-200,+200) | Launch strike against all major NATO cities!	(+50) | Launch strategic nuke against North Dakota and other silos	(-50,-25) | Claim strategic nuke was an accident	58.3%	(-200,+200) | Launch strike against all major Russian targets	(+50) | Launch strategic nuke against Moscow	(-60,-30) | Claim strategic nuke launch was an accident
21	Insensate nuclear use				83.3%

Figure 2) Basic Block Diagram of a Single Game Card

Figure 3) First Three Rounds of NATO Game Cards

Figure 4) First Three Rounds of Russian Game Cards