There exists a rich history of language game modelling starting in the mid nineties by Luc Steels (Steels, 1995,1996) and continuing today. I will focus on a set of key lexical language games that have, over the past two decades, dramatically increased our understanding of the strategies needed for linguistic conventionalisation, learning and alignment.

In a first part we will focus strategies for the Naming Game, the most well-known and deeply studied language game. One could call it the prisoners' dilemma game of language games. The focal question of the Naming Game is how a population of agents can all agree on the same names for a set of objects. The only means of arriving at such an aligned naming system is to engage in a series of small peer-to-peer interactions called naming games. Each interaction engages two agents, a speaker and a hearer, and the speaker has to draw the attention of the hearer to an object (which both agents see) by uttering a single name for that object. 

A number of strategies have been suggested in the literature. One of the first strategies was proposed by Steels and McIntyre (1999) and was based on frequency in order to reach convergence. Soon after strategies based on lateral inhibition (active damping of competitors) were introduced and since the mid 2000's a wide variety of models from statistical physics have been applied to the Naming Game. The Naming Game has also been applied to different domains  such as the Color Naming Game (Steels and Belpaeme, 2005) and the Grounded Naming Game (Steels and Loetzsch, 2012). 

A second family of lexical language games, known as Guessing Games, shifted the focus to the problem of uncertainty in word learning. Different scaffolds that the Naming Game introduced are lifted in order to tackle increasing levels of uncertainty the agents are faced with. One approach defines the problem of uncertainty as a mapping problem, mapping words to (pre-established) meaning or concepts (Siskind, 1996). A second approach that will be discussed takes a constructivist stance and looks at strategies for the gradual creation and shaping of meaning (Wellens, 2012). 

Baronchelli, A. (2012). The minimal naming game: a complex systems approach. In L. Steels, ed., Experiments in Cultural Language Evolution, John Benjamins, Amsterdam.

Siskind, J.M. (1996). A computational study of cross-situational techniques for learning word-to-meaning mappings. Cognition, 61, 39–91.

Steels, L. (1995). A self-organizing spatial vocabulary. Artificial Life, 2, 319–332.

Steels, L. (1996). Self-organizing vocabularies. In C.G. Langton & K. Shimohara, eds., Proceeding of the Fifth International Workshop on the Synthesis and Simulation of Living Systems, MIT Press, Cambridge, MA.

Steels, L. & McIntyre, A. (1999). Spatially distributed naming games. Advances in Complex Systems, 1, 301–323.

Steels, L. & Belpaeme, T. (2005). Coordinating perceptually grounded categories through language: A case study for colour. Behavioral and Brain Sciences, 28, 469–489.

Steels, L. & Loetzsch, M. (2012). The grounded naming game. In L. Steels, ed., Experiments in Cultural Language Evolution, John Benjamins, Amsterdam. 

Wellens, P. & Loetzsch, M. (2012). Multi-dimensional meanings in lexicon formation. In L. Steels, ed., Experiments in Cultural Language Evolution, John Benjamins, Amsterdam.