7.20 - Coordination & payoff irrelevant cues

Claims of Schelling

In pure coordination games, payoff-irrelevant cues make some strategies “salient” / some ways to coordinate “focal”

PICs help coordination in mixed-motive (opposite interests) coordination games of real importance

• e.g. military strategy,

help agreement in bargaining/resource division

• especially when there is a common interest in reaching some agreement.

Isoni et al. (2013) - OV

Studies if payoff-irrelevant cues help make some ways of coordinating “salient” or “focal” in bargaining over division of resources

1-shot coordination games in lab with mixed motives

• common interest in reaching some agreement

• BUT opposed interests over which agreement.

Bargaining table game - both see same

• games differ in no. disks + value of disks + location

Coordination success measures:

• Focus on agreement rate (% of pairings with agreement)

• OR earnings efficiency index (avg across all pairings of: combined payoffs achieved / total of disk values on table

Isoni et al. (2013) - Bargaining table

2 player game with fixed pairs + 24 rds

• no feedback between games

Each has a base

Disks of monetary value across board - players can claim any disk

• bargaining is tacit - independent claims with no comms

If disk only claimed by 1 player then they get the value otherwise no one does

2 potential sources of inefficiency:

• Failure to agree: If any disk is claimed by both players, they both get zero (in total).

• Failure to claim all disks: Disks not claimed by either player are “wasted”

Disk locations - PIC controlled by experimenter

• observable to both + doesnt change value

Incentives - For each pair, one game selected at random; players get outcome of that game

• So, each game is, in effect, a one-shot game.

Isoni et al. (2013) - Schelling hypothesis

Both claiming none OR all is weakly dominated strategy so coordination needed to decide who picks what

Players will use payoff-irrelevant cue from Rule of Proximity which says:

• If a disk is nearer to your base than to the other base then subject claims it

Both players see (and know the other sees) game via bargaining table display and note cues it provides

When PIC less obvious (equidistant from both) → less coordination → lower payoffs

If locations only salient guide, then both players have interest in following it

• Even less favoured player if no other way to increase prob of achieving agreement

“Beggars cannot be choosers about the source of their signal, or about its attractiveness” - Schelling

Isoni et al. (2013) - Example

Equal design apart from proximity

Red favoured - earns 13% more on avg

Earnings efficiency index higher for game 1 (65% vs 48%)

In line with Schelling hypotheses

• when proximity rule doesnt apply EEI & agreement rate drop a lot

  • EEI 18.5% & AR = 27%

Bargaining table pros

• Simple representation of games

• Clear distinction between payoff-relevant and payoff-irrelevant factors

• Controlled manipulation of whether Rule of Proximity does or does not give advice on which disks to claim

Shows any bargaining may have PICs which can aid agreements

• Not necessarily Rule of Proximity but PICS in general

PICs and communication

Fear influence of payoff-irrelevant cues wont survive if players could communicate

• Is PICs role just an artefact of ‘tacit’ coms

• Communication allows bargaining that is more than tacit

If cues seem arbitrary to player not favoured by them, that player might use communication to challenge their authority

• Now player can appeal to fairness

Isoni et al. (2014) - OV

Adds limited communication to 2013 game (comms player-player)

• Either player can provisionally claim (and cancel any claim) any disk at any time

• All current claims of both players visible to both players,

  • with highlight for disks currently claimed by both;

• Each player can explicitly “accept” the current claims (but can cancel acceptance)

• Game ends if both players are “accepting” at same time or time runs out.

Payoffs determined as in previous design using the final claims, whether explicitly agreed or not.

Different set of bargaining tables used

Very flexible comms as communication emerges spontaneously

Isoni et al. (2014) - possible effects of comms

May weaken impact of disk location on final division

Strengthen role of fairness considerations;

Make it less likely that any disks will be unclaimed OR disks claimed by both players.

Isoni et al. (2014) - RESULTS

Strong tendency for bargains to emerge that are efficient (all disks claimed, none by both players)

• Either yield equal payoffs or as close to equal as is possible if efficiency achieved

Comms enhance use of fairness considerations, relative to payoff-irrelevant cues.

RoP not often followed when would conflict equal payoff (even extreme RoP)

• BUT very common when can mediate equal payoffs

• PICs still relevant and easy option to choose out of all possibilities

Coordination summary

Disequilibrium payoffs matter as well as equilibrium payoffs

Available actions and the possible payoffs from them matter

• BUT are not the only factors affecting behaviour

Player’s expectations of the play of others matters critically

• Shaping expectations can be important:

  • contextual PICs + history + belief-shifting events + communication.

  • All these may align expectations in helpful or unhelpful ways