The king and the towns against the barons
The defining characteristic of feudalism was military decentralization. The king held no monopoly of legitimate violence; he depended on the armed retinues of his vassals. That dependence built a check on royal power into the system — and it left a door open.
Smith's way through that door was a three-way relationship between lords, towns, and the king. He envisioned the relationship between towns and lords as inherently conflictual, and saw in that conflict the basis of an alliance:
The burghers naturally hated and feared the lords. The king hated and feared them too; but though, perhaps, he might despise, he had no reason to either hate or fear the burghers. Mutual interest, therefore, disposed them to support the king, and the king to support them against the lords. Wealth of Nations, Bk. III, Ch. 3
This paper restates that analysis in the language of game theory — and shows that Smith's equilibrium is one of several possible outcomes. A review of the historical record reveals that all three alliances occurred. Towns sometimes allied with lords against tyrannical kings. Kings sometimes allied with lords against overly independent towns.
What each player brings
The three players are asymmetric in a way that does most of the analytical work.
The King
Legitimacy without overwhelming material power. Sacral authority made him hard to displace, but he ruled through a coalition — a network of bargains with magnates and towns — not by bureaucratic fiat.
The Lords
Independent military capability. Each lord controlled his own armed retainers, fortified castles, and local justice — and could defect from the royal coalition with those resources intact.
The Towns
Commercial wealth, defensive but not offensive military capacity, and a desire for self-governance. Towns could fund a king and man their own walls — but never threaten his throne.
It is this asymmetry — towns valuable as allies, harmless as rivals — that made the king–town alliance mutually attractive whenever the lords threatened both. It is also why the alliance could not last.
The model
Three players, i ∈ {K, L, T}. Any two may form a coalition against the third. Payoffs are explicit functions of four state parameters: urban wealth W, royal capacity κ, lordly military power λ, and the royal tax rate τ.
The king moves first, proposing an alliance to either the towns or the lords. The proposed partner accepts or rejects; if rejected, the excluded party may propose the alternative coalition. The game is solved by backward induction; the equilibrium concept is subgame-perfect Nash equilibrium. Where no coalition forms, the status quo SQ obtains — continued feudal disorder, assumed to be Pareto-dominated by all three coalitions.
Coalition solver
| Coalition | πK | πL | πT |
|---|
The switching condition
The king prefers the towns to the lords when the net gain from the town alliance exceeds the cost of fighting the lords plus the support forgone by not allying with them:
| Coalition | King's condition | Partner's condition | Historical context |
|---|---|---|---|
| KT | W > W*(λ, κ) | s − sL > (τ − φ)W | Philip Augustus; Smith's conjectural history |
| LT | — | h > r + cK(κ) | Magna Carta (1215); War of the Public Weal (1465) |
| KL | W < W*(λ, κ) | r > h − cK(κ) | Frederick II; Eastern Europe |
The threshold W*(λ, κ) is rising in λ — when lords are more powerful, towns must be richer to justify fighting them — and falling in κ, since a stronger king finds the lords cheaper to subdue. That single boundary does most of the comparative-static work, and reappears in Section IV as the frontier the dynamics push against.
Historical evidence
All three coalitions occurred. Each case below loads its parameter configuration into the solver above.
Charters as commitment technology
Town charters are where the model's abstractions touch the documentary record. The grant by Louis VI to Lorris — later extended to scores of communities in the royal demesne — specified that residents would pay only fixed rents, be quit of all taille and forced exactions, owe one day of local military service, and be protected from purveyance. Fines were strictly limited; no one could be molested travelling to or from market.
In the language of the model, a charter raised s(κ, λ) by replacing arbitrary exaction with predictable obligation, making royal protection credible. What it created was a territorial immunity — a settlement living under a special law guaranteed by a holder of regalian powers. In return the chartered town supplied fiscal revenue and military support, raising both m(W) and τW. That is what made the KT coalition attractive to the king.
Note the corollary: lords chartered towns for exactly the same reasons. By the mid-thirteenth century a craze for urban development had spread to every corner of France, with counts, dukes, and lesser lords all competing to charter villes neuves and bastides. The presence of a charter therefore does not predict allegiance to the king rather than to a lord. Both sides used chartering as a tool of coalition-building.
Magna Carta: credibility as the binding constraint
Towns switch to the lordly alliance when the tax savings from escaping royal taxation, plus lordly protection, exceed royal protection. For 1215 it helps to decompose lordly protection as sL(λ) = θ(λ)·R, where R is the value of the rights promised and θ the credibility of the lords' commitment to deliver them. The content of the barons' offer mattered only insofar as the offer was enforceable.
John imposed a high effective tax rate but also provided security, so the credibility threshold θ* stayed high and London stayed loyal despite real grievance. Two things then moved together. Bouvines (July 1214) cut κ sharply, which lowered s(κ, λ) and so lowered θ*. And the barons did something with little precedent: they wrote the charter down, with an enforcement mechanism — the committee of twenty-five — which raised θ.
The City of London shall enjoy all its ancient liberties and free customs, both by land and by water. We also will and grant that all other cities, boroughs, towns, and ports shall enjoy all their liberties and free customs. Magna Carta, 1215 · clause 13
Threshold down, credibility up: θ > θ*. The largest town in England switched, and London's support proved decisive at Runnymede.
Urban loyalty in the War of the Public Weal, 1465
A striking feature of 1465 is that different regions saw different equilibria emerge simultaneously. Loyalty tracks princely territories, not distance from Paris.
Dynamics and the diamond-buckle puzzle
Smith's account is not static. The alliance between king and towns does not merely persist — it transforms the conditions that gave rise to it.
Play the stage game repeatedly. Players are myopic: they pick the coalition that maximizes current-period payoffs, which is a natural assumption for medieval politics, where dynasties ended, lords were killed or dispossessed, and town governments turned over. The coalition that forms then determines how the state variables move.
Under KT, urban wealth grows because royal protection lets commerce flourish; royal capacity accumulates out of tax revenue; and lordly military power falls in proportion to urban wealth. That last term is Smith's celebrated mechanism — lords "gradually exchanged their whole power and authority" for "trinkets and baubles."
All for ourselves, and nothing for other people, seems, in every age of the world, to have been the vile maxim of the masters of mankind. … For a pair of diamond buckles, or for something as frivolous and useless, they exchanged the maintenance, or what is the same thing, the price of the maintenance of a thousand men for a year, and with it the whole weight and authority which it could give them. Wealth of Nations, Bk. III, Ch. 4
Phase diagram in (W, λ) space
Or click anywhere on the phase diagram to place the polity by hand.
Why the two equilibria are asymmetric
Under KT the system moves right and down. Rising W pushes it deeper into the KT region; falling λ lowers the boundary, reinforcing its position; growing κ lowers the boundary further still. In the short and medium run the king–town alliance is self-reinforcing. In the long run the same decline in λ carries the system below λ̲, the lords cease to matter, and urban privileges become grants from above rather than bargains between equals. This is the world of early modern absolutism — a canonical self-undermining institution, in Greif and Laitin's sense.
Under KL the system moves left while λ is preserved. Urban wealth stagnates, so towns become still less attractive as allies; commerce does not develop, so lords are not tempted by luxury spending and keep their retinues. The configuration reproduces itself. This is a poverty trap: towns that start weak stay weak, lords that start strong stay strong.
The asymmetry generates divergence from similar initial conditions. Small differences in W₀, amplified by the self-reinforcing logic of whichever coalition forms, produce dramatically different long-run trajectories — commercial development and eventual absolutism in one case, the second serfdom in the other.
What the boundary leaves out
As derived, the switching boundary treats regime change as frictionless. In practice accumulated institutional relationships create switching costs that make it sticky. A town whose commercial networks, governance structures, and political relationships are built around one patron faces real costs in switching to another, even where current payoffs would favour defection. In 1465 the Loire towns stayed loyal not because the king rewarded loyalty but because their economic and institutional lives were oriented toward the royal domain — while Bourges, Rouen, and Dijon had commercial ties to ducal households that made defection to the royal cause costly. The system must be pushed not merely across W* but far enough across to overcome the weight of existing relationships.
Smith's text and the model's parts
The formalization earns its keep only if each object in it answers to something Smith actually says. The concordance below is the audit.
| Smith | Object | What it does |
|---|---|---|
| “in those days the sovereign of perhaps no country in Europe was able to protect … the weaker part of his subjects from the oppression of the great lords” | λ, κ | Military decentralization: royal capacity is small relative to lordly power, so protection is not a given but a service the king must be able to afford. |
| “he had no reason to either hate or fear the burghers” | m(W) | Towns supply support without posing a threat — the asymmetry that makes the KT coalition attractive rather than merely available. |
| “establishing magistrates and a town council in every considerable town of his demesne” | s(κ, λ) | Chartering as commitment technology: arbitrary exaction replaced by predictable obligation makes royal protection credible. |
| “making the inhabitants of those towns … march out upon proper occasions to the assistance of the king” | m(W) | Urban militias as the military half of the exchange, alongside the fiscal half, τW. |
| “gradually exchanged their whole power and authority” for “trinkets and baubles” | ∂λ/∂W < 0 | The diamond-buckles mechanism, and the engine of the whole dynamic argument: commerce disarms the lords. |
| “A regular government was established in the country as well as in the city, nobody having sufficient power to disturb its operations” | λ < λ̲ | The absolutist terminus: with the lords irrelevant, the three-player game collapses and urban privileges become grants from above. |
| “the cities generally became independent republics, and conquered all the nobility in their neighbourhood” | κ < κ̲ | Smith's own limiting case — Italy and Switzerland — where the king drops out and the game reduces to towns against lords. |
Complications the framework does not carry
Towns were not unitary. In early fourteenth-century Flanders, Bruges, Ghent, and Ypres were split between the Leliaerts — wealthier merchants and patricians who backed Philip IV — and the Klauwaerts, artisans and guildsmen who sought representation and allied with the Count of Flanders against the French crown. Where towns are internally divided the relevant question is not whether towns ally with king or lords, but which faction within them forms the dominant coalition.
Nor were the lords. During the Magna Carta crisis roughly two-thirds of the leading barons joined the rebellion; at least a third stayed loyal to John. And by the later Middle Ages the instinctive class hostility Smith describes had given way — the French nobility of 1465 understood perfectly well the value of urban support.
The peasantry is absent. The Jacquerie of 1358 and the Comuneros revolt of 1521 both work as KL episodes only because an external shock made towns threatening to lords and crown alike. Modelling that properly needs a fourth player.
And the scope closes around 1600. After that, Paris at 400–500,000 and a rapidly growing London posed a new kind of threat: not chartered magistrates bargaining with a king, but an urban crowd that could mobilize directly. That is a different game, and well beyond Smith's analysis.
What the framework does explain
Not why some regions had weak kings and others strong ones, or why some towns were richer than others — those are prior questions about geography, trade routes, military technology, and contingency. What it explains is how, given a configuration of parameters, coalitions formed and reformed; and how shocks to those parameters could tip a society from one equilibrium to another, with consequences that then persist and amplify.
One implication is worth stating plainly. The medieval urban liberties were inherently temporary. They arose from a particular configuration of power — weak kings, strong lords, growing towns — that could not persist indefinitely. Once the lords were weakened, the bargain that sustained urban privileges dissolved. Which may be why the constitutional achievements of the medieval period so often proved fragile in the face of early modern state-building.