Kudrinski jaeger egt

Evolutionary Game Theory and
Linguistic Typology: a Case Study
Gerhard Jäger

CONSIDER all possible case marking types that
only use case splits induced by the contrast
between pronouns and full NPs

THE MAIN FUNCTION OF CASE MARKING is to
disambiguate: enable the hearer to identify the
argument roles A (agent, the transitive subject)
and O (the direct object)

SPEAKER wants to disambiguate and use as few
case morphemes as possible
SPEAKER STRATEGY:
any function S from M(eaning) to F(orm)

HEARER wants to correctly understand the
utterance
HEARER STRATEGY:
any function H from F(orm) to M(eaning)

COMMUNICATION is successful if the hearer (H)
recovers the intended meaning m from the
observed form

SPEAKER UTILITY:

Here k formalizes the priorities of the speaker

HEARER UTILITY

WE ARE DEALING with elementary transitive
clauses: two NPs, A(gent) and O(bject), both
may be either p(ronoun) or n(oun)

NATURE chooses the word order A-O and O-A
with a 50% probability each. Furthermore
nature specifies which of the two NPs is A and
which is O, and whether they are n or p

CASE MARKING patterns (speaker strategy):
1) Pronominal subjects
2) Non-pronominal subjects
3) Pronominal objects
4) Non-pronominal objects

EXAMPLES: zzaz (English), eezz (Basque)

16 case patterns
eeaz zzaz
eeza zzza
eezz zzzz
eeaa zzaa

zeaz ezaz
zeza ezza
zezz ezzz
zeaa ezaa

eeaz zzaz
eeza zzza
eezz zzzz
eeaa zzaa

zeaz ezaz
zeza ezza
zezz ezzz
zeaa ezaa

HEARER always interprets e -> A and a -> O

AMBIGIOUS clause types:
p/z – p/z
n/z – n/z
p/z – n/z
n/z – p/z

HEARER strategies only differ with respect to the
meaning they assign to 3. and 4.

1. p/z – p/z (not relevant: the same payoff)
2. n/z – n/z (not relevant: the same payoff)
3. p/z – n/z
4. n/z – p/z

-> 4 possible strategies: AA AO OA OO

zzaz/AO zzaz/OA zzaz/OO zzaz/AA
zzza/AO zzza/OA zzza/OO zzza/AA
eezz/AO eezz/OA eezz/OO eezz/AA
zzzz/AO zzzz/OA zzzz/OO zzzz/AA
zzaa/AO zzaa/OA zzaa/OO zzaa/AA
zeaz/AO zeaz/OA zeaz/OO zeaz/AA
zezz/AO zezz/OA zezz/OO zezz/AA
ezzz/AO ezzz/OA ezzz/OO ezzz/AA

FOR small values of k
*strict NE *non-strict NE

FOR larger values of k
*strict NE

FOR very large values of k
*strict NE

THE SYSTEMS that very excluded are
typologically unattested or at least very rare

EIGHT SYSTEMS that give rise to an NE in some
configuration are present
zzaz English zzza Nganasan (only!)
zezz Adyghe ezzz Wakhi (only!)
zeaz Dyrbal eezz Basque (rare)
zzzz Bantu zzaa (rare)

EVOLUTIONARY Game Theory (EGT):
populations of players that are programmed for
a certain strategy

PLAYERS replicate and pass on their strategy to
their offsprings

But grammars are not transmitted via genetic
but via cultural inheritance

replicator dynamics -> imitation dynamics

IMITATION DYNAMICS:
Players are not mortal and have no offsprings

The probability that a certain strategy is imitated
is positively correlated to the gain in average
utility -> successful strategies will tend to
spread, unsuccessful will die out

A strategy pair is evolutionary stable
iff it is a Strict Nash Equilibrium

The NEs using a pure case marking strategy
(zzaa, eezz) are never strict -> not stable

zzza/OA and ezzz/OA each coexist with a well-
attested SNE, that have higher average utility

-> only four strategies are evolutionary stable:
split ergativity, differential subject marking,
differential object marking, and absence of case
marking;
exceptions should be diachronicaly unstable

Kudrinski jaeger egt

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