Language as an interaction cost: An empirical study of immigrants’ literacy performances based on their origin language

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Introduction 
 
There are currently 7.168 languages in use today, only 23 of which account for more than 
half of the world’s population (Eberhard, Simons and Fennig, 2023). Such a variety 
indicates that language is embedded in human development history and that it may have 
evolved concurrently with the genetic evolution of the human species. Pakendorf (2014) 
argues that the evolution of languages has common traits with that of genes, namely the 
vertical line of transmission and the retention of traces of past events. The idea is that, as 
for genes, language is passed down from one generation to another creating, generation 
by generation, a unique set of genes as well as a unique language spoken by that specific 
population. Moreover, genes and languages can get mixed up when parents of two 
different genetic and linguistic groups generate offspring. The chronological history of 
languages, called glottochronology, can help discover the relationship between languages 
and, in a broad sense, also the relationship between different human communities. 
Although being part of human evolution, language seems an element so familiar and 
present in everyday life, even in the most insignificant events and interactions that may 
occur, yet it is an incredibly complex notion to define. Its brief definition is that it is a 
system of conventional spoken, written or signed symbols, used as means of 
communication by members of a social group; note, here, the use of the word 
“conventional”, which will be later defined more in depth. Such a definition does not, 
however, include the incredible variety of them. Do different language systems have a 
common base, with slight variations among each of them, or are they each an isle with no 
connection to other communication systems? Chomsky’s (1957) theory of language, for 
example, asserts that some linguistic abilities are innate to humans, so that there may 
exist a universal grammar for every existing language. It is out of the scope of this work 
to determine how languages were born and whether they are innate to humans. However, 
one interesting characteristic of languages is the previously mentioned “conventionality”. 
A set of rules established over the course of human history, difficult to trace back, 
however known to every member of a group that speaks the language. We will treat 
language as a convention in the broader game theoretic framework of coordination 
games. Thus our underlying assumption about the origin of languages is that they have 
formed as the result of indefinitely repeated interactions (games) among players with the 
ultimate payoff of communicating effectively with one another. Those countless
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interactions have given rise to strategies that were more effective than others in 
conveying a message to the “opponent” player, so that every other successive player 
decided to adopt that same strategy in their round of interaction, until such strategy 
became the norm or, in other terms, the convention of language. Every distinct population 
developed their very own convention of communication, different from that of other 
groups. What happens, then, when two different languages come into contact? Will there 
be one that will supersede the other or will both of them survive? There will be 
contaminations, but in which direction? The kind of interaction between two individuals 
or groups of them that speak different languages will be called a “language game”, in 
which players will have to choose the language to speak with the opponent(s). In some 
cases, players will as well have the chance to become bilingual, therefore to learn a new 
linguistic convention. 
We will describe the issue starting from the general context of coordination games. 
Chapter 1 will address the question of what a coordination game is and how cooperation 
can arise from typically non-cooperative setting, despite the existence of an opposite 
major force, that of competition. From an evolutionary viewpoint, competition and 
coordination are both essential to survival and, as will be established further in the 
chapter, the first is necessary for selecting the fittest individuals among groups while the 
latter is an efficiency enhancing mechanism among individuals of the same group. There 
are different strategies that improve the possibility of cooperation arising as the ultimate 
equilibrium in the interactions among different players, that include reciprocating directly 
one’s opponent (direct reciprocity) with the same action they addressed, reciprocating an 
opponent based on their actions toward other individuals (indirect reciprocity) or only 
being “nice” to the neighbours closest to a player (spatial reciprocity). From these simple 
rules which promote cooperation among players of these cooperation games, there are 
cases where one of the former becomes much more than a rule: it becomes a convention, 
something played over and over by every player entering the same kind of interaction, 
because it is known by every player and is known to lead to a cooperation equilibrium. 
Thus language will be analysed as the result of a repetitive interaction of which aim is 
communication, so that it becomes a convention, a set of rules known by every individual 
player trying to communicate and expected to be played by every other player. 
Subsequently, a language game and its variations will be described in chapter 2, 
accounting for the peculiar assumptions that constitute the language game. Players of the 
language game will want to coordinate, but they will have different preferences on which
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of the two available equilibria (i.e. languages) to do so. One variation of such a game is 
the bilingual game which, besides the two previous equilibria, will allow for a mixed 
equilibrium, in that players will have the possibility of choosing to learn or speak both 
languages, thus becoming bilingual. Such a choice will come with an additional cost, 
nonetheless, that will modify the possibility of a bilingual outcome based on how high (or 
low) such a cost is for each player. The cost of flexibility represents the key feature in this 
work, as we will attempt to analyse the impact of it on the interactions between two 
different linguistic groups, more specifically immigrants and natives of a host country. 
This chapter contains, therefore, the theoretical framework of the game theoretic 
approach to language and to the interaction between different languages. The developed 
idea consists in considering destination language proficiency as an indirect measure of 
the flexibility cost previously introduced in the theoretical model, coming from different 
origin languages. Chapter 3 will, thus, introduce the empirical framework. Linguistic 
proficiency influencing factors will be described, as per the most recent literature on the 
subject, among which one of them is represented by the linguistic distance between the 
origin and the destination languages. This will be the focus of the empirical analysis 
carried out in the subsequent chapter. Economic and academic performances of 
immigrants based on linguistic proficiency will be reviewed. The final chapter will 
contain the empirical analysis, the intention of which is that of empirically test the 
language model described in previous chapters. More specifically, the aim is that of 
testing linguistic distance as being a cost of interaction between two individuals (or 
groups) of different languages. The larger the linguistic distance, therefore, the higher the 
cost of interaction (or the flexibility cost). Considering that the language game model 
prescribes less interactions with the other language group for high flexibility costs and 
more coordination equilibria with the other language group for lower cost level, we 
hypothesize for our empirical analysis that the more distant two languages are, the less 
proficient one group will be in the others’ group language. Put in other terms, immigrants 
whose origin language is very different from the host country language will also be less 
proficient in the latter, which will be an indicator for fewer interactions with natives with 
respect to immigrants who speak an overall similar language to that of the host country. 
The analysis will be carried on using data from the OECD Programme for the 
International Assessment of Adult Competencies (PIAAC) taking Spain as the host 
country and Spanish as the destination language to which 13 different origin immigrant 
languages will be compared. Linguistic proficiency is difficult to measure, therefore we
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will assess it through the means of literacy performances of adult immigrants.
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1. Cooperation, social conventions and coordination failures 
 
1.1. Cooperation as opposed to competition 
 
A game theoretic framework takes into account strategic interactions among players, in 
which the objective of each of them individually is to maximize the payoff deriving 
from such an interaction. Standard non-cooperative game theory is set so that the game 
can only be played once, with players being rational and having complete information 
about the opponent’s preferences and the game itself and that the option of negotiation 
is absent, leading players to rely on self-enforcing agreements (Weibull, 1995;Van 
Damme, 2014). 
Competition has been considered, since the Darwinian theory of evolution (Darwin and 
Kebler, 1859), the main mechanism that influenced and led the evolutionary process 
among species, which closely followed the notion of “survival of the fittest”. Similarly, 
to this concept of evolution and survival in the natural world, the social sciences 
environment and namely, economics, competition represents the driving force 
conducting demand and supply to an efficient equilibrium through the action of Adam 
Smith’s (1776) “invisible hand”. Both natural evolution and economics are 
characterized by a scarcity of resources, which have to be split among its agents and for 
which the latter have to “fight”, be it in the literal sense or in its transposition in the 
rules of the market. Hence, the invisible hand represents the incentive of every 
individual to maximise their utility, that is to survive and produce as much offspring or 
simply to use the available resources as much as possible and derive the highest 
possible enjoyment from them. It follows, thus, almost a logical path to take into 
account competition as the first and foremost impulse when analysing the interactions 
among individuals with the intention to predict the ultimate equilibrium that such 
interaction will yield. The most known and cited strategic interaction (from here on 
“game”) in the game theory that involves competition between players is the Prisoner’s 
Dilemma paradox, a non-cooperative non-zero sum game; non-cooperative in that, as 
stated above, players consider their own utility maximisation and elaborate their best 
response, i.e. their strategy, so as to achieve such maximisation independently of the 
strategy adopted by their opponent. A classic one-shot Prisoner’s Dilemma will lead to 
an equilibrium point (Nash, 1951) where none of the players will benefit ulteriorly by
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modifying their strategy. The latter definition may, at first, suggest that players will be 
content with their decision which, in turn, would mean having maximised the payoffs 
obtainable from the interaction. However, this is not the case in the Prisoner’s Dilemma 
context described above: despite having indeed reached a steady state through rational 
reasoning by both players, the same individually applied logic does not lead to the 
highest potential result. The Nash equilibrium reached in the game is, in fact, an inferior 
equilibrium deriving from the non-cooperative setting of the game. 
Competition is not a negative force per se, in fact it is an often-used principle, both in 
nature, as the means to determine the fitness of survival of an organism, and in other 
human activities not strictly concerning the first one. Without entering in too a specific 
case, it can be said that competition à la Darwin allows to select the elements that will 
best respond to different settings of the surrounding environment. In the economic field, 
the free market represents the gold standard, having the potential to “select” the most 
competitive firms which, once selected, will gain the most profits and have the largest 
share of the market. Cournot’s duopoly model is a typical example of competition 
between two firms, which is none other than a transposition of the Prisoner’s Dilemma, 
for the two firms decide simultaneously the quantity they want to produce in order to 
maximise their profits. The Nash equilibrium occurs when both firms produce the same 
quantity as their opponent. There isn’t a loss in economic terms for the firms which 
would, otherwise, exit the market and not compete anymore as well as in the original 
prisoner’s dilemma game, where players do not get the worst payoff; indeed, the worst 
result is the so called “sucker’s” payoff, obtained by the player who chose to cooperate 
while the opponent has gained a benefit by defecting. Rather, the loss is intended in 
terms of potential payoff that the interaction could have yielded. Such result, however, 
is not reachable when the underlying game is one of competition, because the individual 
interests, although rational, will be in contrast with the collective interest. Indeed, in 
both games, under certain conditions, players would be able to reach a superior 
equilibrium point, but only if the option of cooperating together was available: that is, in 
the Prisoner’s Dilemma, if players could cooperate, the “years in prison” they would 
have to spend would be fewer for both of them, whereas in the Cournot’s duopoly 
model cooperation could lead to the creation of cartels between firms which would 
influence the price of the goods, thus allowing both players to gain in terms of larger 
profits from the agreement. It seems, therefore, that cooperating produces better results 
than not cooperating, but are incentives to do so high enough for individuals, organisms
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or firms to cooperate and help the opponents, in spite of the limitedness of resources 
and, eventually, of the need for everybody to fight for its own survival? Many authors 
would describe cooperation in terms of a pursuit of a higher individual payoff that 
ultimately leads to the wellbeing of all those involved in the interaction as, again, in 
Smith’s invisible hand which, on the one hand allows to reach an efficient market 
equilibrium while implying, on the other hand,  that such an efficiency will derive from 
the selfish interest of individuals who will achieve a socially optimal market 
equilibrium, although acting to maximise their own utility. Within the field of animal 
behaviour, for instance, Grafen (1984) describes a “self-interested refusal to be spiteful” 
while West-Eberhard (1975) defines a “quasi-altruistic selfishness”. All of these 
definitions denote an underlying selfishness, which manifests itself through a 
competitive behaviour that, however, is bound by the willingness to achieve higher 
levels of utility for oneself and yields, as a by-product, a higher wellbeing for the rival 
party as well. Whichever the reason behind the altruistic behaviour, players decide to 
change their myopic selfish response in favour of an action that will benefit the group as 
a whole. The main approaches that have been used to explain the function that 
cooperation could have in evolutionary terms are kin selection and reciprocal aid, the 
first being rooted in genetics, therefore directly connected to the reproductive success of 
individuals that carry the same genes; the other approach entails a weaker connection 
among individuals and imply no expectations of an immediate compensation in 
exchange of an altruistic behaviour. Rather, players are rewarded, or have a higher 
probability of being rewarded, the more altruistic interactions they engage in and, 
consequently, the better reputation they build for themselves. 
Although it may seem that cooperation is a superior strategy to competition, both forces 
are needed in order to determine the fittest individuals that will survive the surrounding 
environment. Neither competition nor cooperation can survive alone as pure strategies. 
Inside the evolutionary game theory analysis, these actions co-exist in a specific ratio, 
such that there will be a proportion of population that will cooperate until the benefits 
from doing so exceed the individual costs of cooperating, while the rest of the 
population will behave as defectors, reaping the advantages of cooperation without 
contributing to it in what is called the “temptation reward”. This kind of mixed 
strategies dynamic equilibrium will constitute an evolutionary stable equilibrium (ESS), 
that is a situation where no individual in the population will have additional benefit by 
changing their strategy. In other words, one can say that this type of strategy is
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uninvadable (Taylor and Jonker, 1978; Axelrod and Hamilton, 1981; Frank, 2003; Bach 
et al., 2006). Altogether, competition may serve as a selection mechanism for the fittest 
among different groups, while cooperation may be an efficiency enhancing mechanism 
in a group of similar individuals (Leigh, 2010; Alexander, 1987). 
  
1.1.1. Repeated games 
 
Although having positive implications for all the players that participate in the 
interaction, cooperation requires specific conditions for it to occur. A typical Prisoner’s 
Dilemma situation would not turn out to have a different outcome unless the 
circumstances under which the game evolves were different. Namely, what seems to be 
fundamental for a cooperative behaviour to arise is the repetition of an interaction. One-
shot games give players the incentive to maximise their own utility, in spite and 
independently of what the opponent’s response will be, because players do not feel 
compelled to respect any agreement, as there doesn’t exist one. Repeating an 
interaction, on the other hand, enables players to retaliate in subsequent interactions if 
the effective outcome they obtain is less than the potential one because of an unfair 
behaviour of the counterpart. These type of games provide, therefore, a simple form of 
self-enforcing agreements between players (Pearce, 1992). Again, taking the Prisoner’s 
Dilemma game as a reference, players do not have an incentive to cooperate when 
playing the one-shot game; however, it has been proven that when playing repeatedly 
the interaction, both players are more likely to cooperate. Nonetheless, repetition alone 
is a necessary but not sufficient condition for cooperative behaviour to occur. In fact, if 
the game were to be played a finite number of times and both players knew the number 
of repetitions, cooperation would not arise. This is because the problem would be solved 
by backward induction (Luce and Raiffa, 1957) leading rational players to defect at 
every stage. Hence, for cooperation to be a possible outcome, interactions have to be 
repeated an infinite or an indefinite number of times. A second element that can 
determine a cooperative outcome is how patient players are. Being more patient is 
beneficial for the player, as it will allow to build a reputation for which the player will 
be known as more cooperative. More importantly, however, is that patience, also called 
the “discount factor” of players, allows cooperation to become a feasible and stable 
strategy in a repeated game (Friedman, 1971; Abreu et al., 1994). 
Although repeated games models may explain the modalities in which cooperative