Endless Games: Domestic Constraints, Structural Suboptimality, and Who Fills the Gaps
Win-sets, regime types, and the arithmetic of gaps when the guarantor withdraws.
In a piece published here earlier this year, I argued that Trump’s negotiating style is best read as a local symptom of a structural collapse in the international system’s discount factor — and that a third actor, China, was positioned to benefit from the resulting predictability premium. The model was clean: A defects, C holds steady, others recalibrate their expectations and shift strategic weight toward the more reliable player. I ended with a conjecture: that China might not just be holding steady but quietly defecting toward Iran, selling military satellites to a theocratic regional power that controls the Strait of Hormuz.
On April 15th, the Financial Times confirmed something close to it. TEE-01B — a high-resolution Earth observation satellite purchased by Iran’s Islamic Revolutionary Guard Corps in 2024 for $36.6 million — was actively used during the March war to target American bases in the Gulf. The conjecture was not wrong. But the bigger picture it revealed was more complicated than my original model could handle.
Two recent interventions helped me see why. Andrew Sharp, a foreign policy analyst writing on SharpText, published Beijing Is Not Playing the Long Game on May 1st — a sharp, empirically grounded argument that China is not patiently accumulating advantage but is trapped in reactive, suboptimal strategies by its own internal constraints. Simone Pieranni, who covers Chinese and Asian affairs for the Italian podcast Altri Orienti, documented the same dynamic from a different angle in a late March episode: after the Epic Fury operation on February 28th and the selective closure of Hormuz, China was forced to play three incompatible tables simultaneously — sole buyer of Iranian oil, strategic partner to Gulf monarchies, and indispensable commercial interlocutor for a Washington that needed it before the midterms. The degrees of freedom available to Beijing were drastically reduced.
Both pieces sound, on first reading, like a refutation of my earlier argument. If China is systematically forced into suboptimal strategies, the predictability advantage evaporates, and the mathematical structure of the iterated game I described falls apart on contact with reality. I don’t think that’s the right conclusion. I think Sharp and Pieranni describe deviations from the model that the model itself, properly extended, can explain. What follows is that extension. It requires two additional parameters.
The domestic constraint, and why Putnam was right
In 1988, Robert Putnam — the same political scientist who would later write Bowling Alone on the decline of American social capital — published a paper arguing that every leader plays two tables simultaneously: an international one, where they negotiate with counterparts, and a domestic one, where any agreement reached must be ratified by their own constituency. Each leader has a win-set: the range of agreements their base will accept. A deal is reachable only if win-sets overlap. When they don’t, no deal gets signed, even if both sides know perfectly well that cooperation would benefit them.
The uncomfortable corollary, which Putnam noted and Schelling had anticipated in 1960, is that a narrow win-set can be both a constraint and a resource. A leader can hide behind their domestic base — “I can’t, they won’t ratify” — even when they could. Italian prime ministers have used this argument in Brussels for fifty years. It often corresponds to reality. Often it doesn’t. The difference is almost never visible from outside, which is precisely what gives the win-set its strategic utility.
For our purposes, what matters is the constraining use. Let ρᵢ measure the fraction of rounds in which player i is forced to play a domestically constrained move instead of the structurally optimal one. At each round, player i plays the optimal move with probability 1−ρ, and the constrained move with probability ρ. On an infinite horizon, with δ = 0.9, the multiplier on any per-round loss is ten. A ρ of 0.3 — plausible for a large autocracy under structural stress — costs the player one fifth of their total cooperative advantage, even if their time horizon remains long. A ρ of 0.5 costs a third.
Why democracies have lower ρ — and why it matters
My hypothesis is that democracies, under structural pressure, tend to have lower ρ than autocracies. They have, on average, more room to maneuver. This looks counterintuitive and needs unpacking.
Every political regime must continuously manage the dissent that material conditions produce internally. A democracy manages that dissent as a flow: regular elections, alternating majorities, free press, civil society mobilization, elite turnover. The cost of change is paid in small, continuous installments, each metabolizable. An autocracy manages the same dissent as stock: suppressed, pushed underground, accumulated. When accumulation exceeds containment capacity, it erupts discontinuously — purges, violent dynastic transitions, revolutions from above, occasionally regime collapse. The cost of change is paid in default, not installments.
The financial metaphor is structurally accurate. A democracy functions like a fixed-rate mortgage, where structural pressure is gradually absorbed and redistributed over time. An autocracy functions like senior debt with an acceleration clause: while payments are current it looks like the safest instrument in the world; when a payment is missed, everything accelerates at once, and the risk pricing is asymmetric and dramatic.
Hirschman named this in 1970: exit, voice, and loyalty. In a democracy, dissent has access to the voice channel — it can express itself, organize, and in doing so act as a continuous corrective signal to those who govern. In an autocracy, voice is suppressed or heavily filtered; only exit or simulated loyalty remain. The autocratic leader receives distorted or null corrective signals, and the system progressively goes blind to its own pathologies. Acemoglu and Robinson formalized the same point in Why Nations Fail; North, Wallis and Weingast pushed it further in Violence and Social Orders, showing that the transition from limited to open access orders is historically rare, irreversible, and particularly costly when it comes too late.
What this means for ρ is not just that democracies have lower average values — it is that their variance is lower. A democratic regime oscillates in a narrow band around a modest mean. An autocratic regime may appear to have low ρ (the leader executes whatever they want, so the rational move seems accessible), but the variance is high: when accumulated frictions emerge they do so with enormous deviation from optimal behavior, and the political system lacks the gradual instruments to reabsorb them. It is the political equivalent of the difference between a liquid equity — oscillating, but continuously priced — and an illiquid asset: apparently stable for long stretches, then repricing discontinuously, the jump incorporating all the information the market had been unable to digest.
China: structural constraint, not tactical ambiguity
Return to Beijing. Sharp’s central observation — that China is not playing the long game because it cannot, chained to internal constraints that force reactive, suboptimal strategies — is, in my view, essentially correct. What the extended model adds is a structural account of why these constraints have become so binding, and why they have increased rather than decreased over the past decade.
One might object that Chinese strategic ambiguity is not a pathology but a feature — that opacity is a millennial cultural inheritance, Sun Tzu rediscovered, the tributary system reactivated. The objection has a real basis but inverts the causation. The Chinese empire always governed a territory of extraordinary internal complexity — ethnicities, provinces, bureaucratic factions, unstable frontiers — in which the direct move was almost always politically costly. The tributary system was designed around deliberate ambiguity precisely because resolving that ambiguity would have required moves the domestic win-set would not ratify. The strategic culture of indirectness is the adaptive sediment of centuries of governance with structurally high ρ. The culture did not produce the constraint; the constraint produced the culture.
What changes under Xi is not the type of constraint but the degree of freedom. The imperial system could choose to dissolve ambiguity when it suited; Xi, having compressed the internal mechanisms that could have gradually absorbed change, cannot do so without compromising his own legitimation. Under Hu Jintao, China’s ρ was already non-trivial, but it was contained by mechanisms that functioned as local substitutes for democratic installment-paying: leadership rotation, factional plurality within the Party, marginally critical technical press, a relatively vibrant regional capitalism acting as an indirect voice channel. All of this compressed sharply after 2012 and accelerated after 2018 with Xi’s personal consolidation of power.
The brutal summary: China increased its internal autocracy precisely in the decade when it needed maximum domestic flexibility to respond to a global structural transition. The moves that the model — and probably Xi himself — would prescribe as optimal for consolidating China’s systemic position (opening to foreign capital, WTO rules compliance, normalization with Brussels, operational distancing from Russia, internal deflation model reform) are all outside the domestic win-set the regime has built around itself. Beijing is doing exactly what its high ρ forces it to do: supporting Iran below the threshold, maintaining the facade of Gulf neutrality, remaining sufficiently cooperative with Washington to not break the May summit. Three incompatible tables, one win-set, systematically suboptimal posture.
America: Trump is not the cause
The mirror case. My earlier piece treated Trump in an overly individualistic way — as though he had somehow decided to lower America’s discount factor below the cooperation threshold. That was a useful idealization but doesn’t survive serious scrutiny. Trump, in the extended model, is not the cause of American behavior: he is the symptom of a domestic win-set that has changed structurally over thirty years and now constrains American foreign policy to a much narrower set of moves than was available in the 1990s.
The structural pressures producing this shift are identifiable independently of any political judgment about the current administration: Midwest deindustrialization as a consequence of Chinese WTO integration that Washington itself had championed; media fragmentation and the end of liberal television consensus hegemony; accelerating inequality concentrated precisely in the areas most exposed to globalization; the spread of a grievance culture that found political language only in its terminal phase. The MAGA movement did not appear from nowhere in 2016. It was already there for at least fifteen years, as a nameless malaise, made more dangerous by its incubation inside the world’s largest power during a unipolar system in crisis.
The bad news: even if Trump left the scene tomorrow, the American domestic win-set would remain what it is for many years. Win-sets, once consolidated, destabilize slowly. Two or three generational cycles, not one election.
The partially good news: America is still a democracy. Its costs of change are paid in installments, not defaults. MAGA can be contested and eroded election by election. The door to cooperative re-entry is not sealed. It is encrusted. But it exists.
Who fills the gaps
The model at this point explains why China cannot play the cooperative optimum, why America’s reversal requires more than one election cycle, and why Russia — low δ and high ρ simultaneously — has specialized in opportunistic predation. What it does not yet capture is a central phenomenon: certain actors are not merely constrained in what they can do — they are called upon to do things their win-set would otherwise allow them to avoid, because other actors have withdrawn and their vacancies must be filled. Political nature abhors a vacuum.
Let σ measure the probability that actor i finds itself covering a systemic function left vacant by someone else. It is a multiplicative function of three factors: material capacity on that function; domestic constraint specific to it; and systemic compatibility — the degree to which other actors accept the substitute in that role by default. If any of the three is absent, the plug doesn’t fit.
Three cases illustrate the current distribution.
China has high σ on the Iran/Gulf diplomatic brokerage function: absorbing ninety percent of Iranian oil exports gives corresponding commercial leverage; the win-set permits energy-diplomatic brokerage even while constraining more visible political exposure; and even Washington accepts the Chinese role, however reluctantly. The result is that the price at the Strait is now set more in Beijing than in Washington.
Russia has high σ on the energy-logistics function, but with a structural defect: the plug fits but leaks. Capacity is nominally high; domestic constraint on the function is very low (the regime’s internal legitimation now depends on being perceived as an energy power); buyers have no immediate alternatives. But the Power of Siberia 2 won’t be operational before 2030, Russian grain exports fell 29 percent in 2025, and Beijing is already diversifying toward Turkmenistan and Canada. The Carnegie Endowment’s Gabuev and Vakulenko describe Russia as an opportunistic disruptor rather than a credible counter-hegemon. Real plug, low pressure.
Europe has high σ on the procedural-multilateral function — and this is the least obvious case. The eighth European Political Community summit in Yerevan on May 4th: 48 heads of state, first EU-Armenia bilateral, first non-European invited (Canada’s Carney), Zelensky, Starmer, Tusk, Rutte for NATO. The usual commentary would be ironic: Europe talking while the world acts. I think that commentary is wrong. In a system where both autocratic high ρ and democratic-dysfunctional high ρ are simultaneously toxic, Europe’s boring procedural predictability — bureaucratic, slow, manifestly uninterested in dominance — becomes for the first time a plugging virtue. The 48 leaders go to Yerevan not because Europe has coercive levers, but because Europe is the only space where Pashinyan, Aliyev by video, Macron, Zelensky, Starmer and Tusk can sit together without the gathering itself signifying a strong strategic move. Europe’s strength is exactly that the gathering means nothing strident. Carney understood this and asked to participate — first non-European in EPC history.
Ukraine: raising your own ceiling
All the examples so far describe actors playing below their structural ceiling. Ukraine before February 2022 was a structurally peripheral actor in every relevant dimension. The model would have assigned it a low ceiling and left it there.
The Russian invasion activated a mechanism the static model does not predict: in phases of rapid structural transition, a player’s network position is not invariant. It can be modified upward, if the actor builds a new systemic function under existential pressure before others can contest it.
Existential pressure produces a very high discount factor by construction — when survival depends on the next round, there is no rational alternative to long thinking. A war of total aggression zeroes out the domestic constraint on the defense function, because Ukrainian society has implicitly ratified a single win-set (survive) within which every defensive move is inside the consensus. And the combination of emergency, distributed engineering talent, a startup ecosystem, and the necessity of developing low-cost tools to face resource asymmetry produced a specialized capacity — attack and intercept drones at unit costs around $1,000, against Russian assets worth millions — that did not exist as a systemic category before 2022.
Garry Kasparov — former world chess champion, now among the most precise analysts of Russian strategic behavior writing in English, on his newsletter The Next Move with Uriel Epshtein — observed in March that the richest states in the world and the richest in the Gulf were turning to Kyiv for drone defense assistance. ABC News confirmed that the United States, Saudi Arabia, and the UAE had approached Ukraine for interceptor drone procurement. In his May 4th piece Putin Is in Trouble, based on leaked European intelligence, Kasparov documented a Russian leadership increasingly confined to bunkers, with the May 9th parade drastically reduced for the first time in thirty years after Ukrainian drones struck Moscow’s airport and refineries up to 1,500 kilometers from the contact line.
One point must be stated clearly: arguing that Ukraine “seized an opportunity” would be the classic pro-Russian rhetorical framing. Ukraine’s choice was not to become a global drone defense platform. It was not to capitulate in the face of exterminatory aggression. Everything after that was the rational response to a constraint the aggressor imposed. The human cost is entirely attributable to the aggressor. The model, in describing how the aggressed modified its network position, says nothing normative about war. It says the opposite: that certain paths to raising the ceiling are accessible only through costs that no rational actor would choose if they had the alternative of avoiding them. Ukraine did not have the alternative. Putin took it away.
Gerasimov’s doctrine, or: Russia’s offensive on ρ
There is one case the model can read in a way that conventional analysis struggles to capture. Hybrid warfare — active measures in the GRU tradition, electoral interference, dezinformatsiya, the fragmentation of adversaries’ domestic narratives — is not a strategy operating on δ or σ. It is a strategy operating on the adversary’s ρ. Russia under Putin developed a specialized capacity not in building positive power but in raising the domestic constraint of its targets: fragmenting win-sets, amplifying internal fractures, making the cooperative optimal move more politically costly for the adversary.
This is rational for an actor with low δ and high ρ of its own: unable to compete on the iterated payoff plane, it plays downward — lowering others’ ceilings rather than raising its own. The most important property of this strategy, however, is that it works only in opacity. It requires the target not to recognize the source of its own internal dysfunction, and the threat to remain below the threshold of collective rational response.
The open invasion of Ukraine burned that threshold. It lowered European ρ on defense — win-sets that did not ratify rearmament now do. It zeroed Ukrainian ρ on the defense function, generating the systemic plug described above. It degraded Russia’s own energy pluggability by reducing systemic compatibility among countries that could have accepted Moscow as an alternative supplier without political embarrassment. A move designed to operate on a single dimension produced perverse effects on all three simultaneously. The model does not predict this outcome. It explains it.
Three shadows
The first piece introduced the shadow of the future: the pressure that all subsequent rounds exert on present decisions. This piece has been about the shadow of the past: the sediment of structural pressures that have shaped each actor’s domestic configuration over preceding decades, projecting onto the present table as a constraint on available moves even when the present structure would allow wider space.
There is a third shadow. When a central actor withdraws from a function the system cannot leave vacant, the gap it opens projects its own pressure onto the table — not asking others to see the future or overcome their past, but to occupy a place they had not chosen. It is the shadow of the void, manifesting as opportunity while containing an obligation.
Anatol Rapoport was a Jewish Russian-born pacifist and mathematical biologist who spent much of his career at the University of Toronto. In 1980, at a computer tournament organized by political scientist Robert Axelrod, his four-line program — Tit-for-Tat: cooperate on the first move, then mirror whatever your opponent did last — defeated far more complex strategies in an iterated prisoner’s dilemma. His point was not that cooperation always wins. It was that systems sustaining cooperation over time have structural properties that can be identified and measured. Forty-five years later, the argument is worth extending one step: systems hold over time not only because their actors see the future, but because their actors are institutionally capable of responding to what they see, and because systemic functions are structurally covered by those who can cover them. When all three conditions fail simultaneously — which is where we are — the system enters a stable dysfunction: not collapsing, but not restabilizing either. Pareto-inferior equilibria trapped in themselves.
The model does not say whether we are past the point of recovery. Models never answer the questions that actually matter, and this one fortunately is among them. What it says is where to look and what to measure. The three shadows are on the table. They overlap in ways that are not encouraging. But somewhere, under the same light that casts them, a peripheral actor raised its own ceiling by creating a function the system did not know it required. It is worth naming the shadows, because naming them is the first step to measuring them, and measuring them is the first step to doing something sensible about it.
The rest is arithmetic. Just arithmetic.
The Abstract is built on a single, stubborn premise: that what we call abstract — ideas, models, theoretical constructs, the invisible architecture of how we think — is not without weight in the world. It lands. It shapes decisions, institutions, alliances. Sometimes it shapes the trajectory of missiles. Claudio Cammarano writes at claudiocammarano.com.
Essential references
Axelrod, R. (1984). The Evolution of Cooperation. Basic Books.
Gabuev, A., & Vakulenko, S. (2026, January). Russia’s Diminished Standing as a Patron Power. Foreign Affairs.
Hirschman, A. O. (1970). Exit, Voice, and Loyalty. Harvard University Press.
Kasparov, G., & Epshtein, U. (2026, March–May). The Next Move [newsletter].
North, D. C., Wallis, J. J., & Weingast, B. R. (2009). Violence and Social Orders. Cambridge University Press.
Putnam, R. D. (1988). Diplomacy and Domestic Politics: The Logic of Two-Level Games. International Organization, 42(3).
Schelling, T. C. (1960). The Strategy of Conflict. Harvard University Press.
Sharp, A. (2026, May 1). Beijing Is Not Playing the Long Game. SharpText.