Measured Games

After C. T. Bauch and D. J. D. Earn (2004), building on P. E. M. Fine and J. A. Clarkson (1986)

The payoff to declining is produced by a running epidemic rather than fixed, so the equilibrium sits at an interior point below the elimination threshold.

Epidemiology

After W. B. Arthur (1994) and D. Challet and Y.-C. Zhang (1997); phase structure from R. Savit, R. Manuca and R. Riolo (1999)

Reward for joining the smaller group makes any widely held forecast self-defeating. Collective efficiency turns on a single parameter and has a critical point.

Econophysics

After C. J. Barnard and R. M. Sibly (1981); formalised by W. L. Vickery and colleagues (1991)

Exploiting other foragers pays only while it is rare, so the group settles at a stable proportion set by the finder's share and group size.

Behavioural ecology · claims not yet audited

After A. Diekmann (1985), formalising the bystander effect reported by J. M. Darley and B. Latané (1968)

One volunteer suffices, so each member acts less often as the group grows and the chance that nobody acts at all rises with it.

Social psychology · claims not yet audited

After H. S. Gordon (1954) and M. B. Schaefer (1954); institutional response from E. Ostrom (1990)

Effort enters a renewable fishery while any profit remains, so the rent is dissipated and the stock can settle past the point of maximum sustainable yield.

Resource economics · claims not yet audited

After R. A. Fisher (1930); local mate competition by W. D. Hamilton (1967), tested on fig wasps by E. A. Herre (1985)

The rarer sex pays better, which drives parental allocation to equal investment, or to a specific female bias where brothers compete for the same mates.

Evolutionary biology

After S. D. Fretwell and H. L. Lucas (1969); tested on mallards by D. G. C. Harper (1982) and on sticklebacks by M. Milinski (1979)

Foragers free to move settle where returns are equal everywhere, which puts each patch's share of the competitors equal to its share of the food.

Behavioural ecology

After R. M. Anderson and R. M. May (1982); the myxomatosis record from F. Fenner and F. N. Ratcliffe (1965)

Exploiting a host harder transmits better and kills faster, so selection favours intermediate harm. Sharing a host with rivals pushes it higher still.

Evolutionary epidemiology

After the entry game of A. Rapoport and colleagues; laboratory results from J. Sundali, A. Rapoport and D. Seale (1995) and C. Camerer and D. Lovallo (1999)

Every allocation that fills the capacity is an equilibrium and none is selected, yet groups track the capacity from the first rounds while individuals stay erratic.

Experimental economics · claims not yet audited

After H. W. Bates (1862); frequency dependence tested in the field by D. W. Pfennig, W. R. Harcombe and K. S. Pfennig (2001)

A harmless species borrows protection from a dangerous one, and loses it as copies become common, because the predator's memory is what the protection was made of.

Evolutionary ecology

After G. Tullock (1980); laboratory record surveyed by E. Dechenaux, D. Kovenock and R. M. Sheremeta (2015)

Spending buys odds rather than the prize, so competition consumes most of what it is fought over, and in the laboratory rather more than that.

Experimental economics · claims not yet audited

After B. Sinervo and C. M. Lively (1996) and B. Kerr and colleagues (2002); mobility threshold from T. Reichenbach, M. Mobilia and E. Frey (2007)

Intransitive dominance leaves no best response, and whether all three types survive is decided by dispersal distance rather than by the payoffs.

Evolutionary biology

After J. Maynard Smith (1974); asymmetric extension by P. Hammerstein and G. A. Parker (1982)

Both parties pay for the full contest and only the more persistent wins. No fixed commitment is stable, and the equilibrium dissipates the whole prize.

Behavioural ecology · claims not yet audited

After É. Borel (1921); solved in general by B. Roberson (2006)

Fixed budgets are split across fronts taken by the higher bid. No pure strategy survives, and asymmetry pushes the weaker player to abandon fronts rather than spread thin.

Operations research

After J. von Neumann (1928); tested on natural data by I. Palacios-Huerta (2003) and P.-A. Chiappori, S. D. Levitt and T. Groseclose (2002)

Pure conflict with no stable choice, where the theory prescribes an exact mixture. The rare case where professionals were measured doing it, including the randomisation itself.

Sports economics · claims not yet audited

After D. Braess (1968); equilibrium following J. G. Wardrop (1952), with bounds from T. Roughgarden and É. Tardos (2002)

Every driver takes the fastest available route and the network slows down. Added capacity can raise equilibrium travel time for everyone.

Transportation science

After D. W. Diamond and P. H. Dybvig (1983); uniqueness by H. Carlsson and E. van Damme (1993) and S. Morris and H. S. Shin (1998)

Under common knowledge both a run and no run are equilibria. Give each depositor a noisy private signal and the outcome is pinned to a threshold in fundamentals.

Macro-finance · claims not yet audited

After E. C. Capen, R. V. Clapp and W. M. Campbell (1971); laboratory account by J. H. Kagel and D. Levin (1986)

The auction selects the highest estimate, so winning is evidence of having overestimated, and the correction required grows with the number of rivals.

Auction theory · claims not yet audited

After T. C. Schelling (1960); measured by J. Mehta, C. Starmer and R. Sugden (1994)

When the payoffs cannot distinguish the options, people choose what stands out rather than what they prefer, and coordinate far above both chance and their own tastes.

Experimental economics · claims not yet audited

After R. Dawkins and J. R. Krebs (1979); acceptance thresholds from N. B. Davies, M. de L. Brooke and A. Kacelnik (1996)

Better mimicry favours choosier hosts and choosier hosts favour better mimicry, but since any rejection rule also throws out some of the host's own eggs, accepting a good forgery can be correct.

Coevolutionary biology · claims not yet audited